Journal of Structural Biology 180 (2012) 132–142

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Journal of Structural Biology

journal homepage: www.elsevier .com/ locate/y jsbi

Improving the quality of electron tomography image volumesusing pre-reconstruction filtering

Mauro Maiorca a,b, Eric Hanssen b,c, Edmund Kazmierczak d,⇑, Bohumil Maco e, Misha Kudryashev f,Richard Hall g, Harry Quiney b,h,⇑, Leann Tilley a,b,⇑a Department of Biochemistry and Molecular Biology, Bio21 Molecular Science and Biotechnology Institute, The University of Melbourne, 30 Flemington Road, Melbourne, Vic.3010, Australiab Australian Research Council Centre of Excellence for Coherent X-ray Science, The University of Melbourne, Melbourne, Vic. 3010, Australiac Electron Microscopy Unit, Bio21 Molecular Science and Biotechnology Institute, The University of Melbourne, Melbourne, Vic. 3010, Australiad Department of Computer Science and Software Engineering, The University of Melbourne, Vic. 3010, Australiae Department of Biochemistry, La Trobe University, Bundoora, Vic. 3086, Australiaf Center for Cellular Imaging and NanoAnalytics (C-CINA), Biozentrum, University of Basel, Switzerlandg Melbourne University Virtual Environments for Simulation, The University of Melbourne, Vic. 3010, Australiah School of Physics, The University of Melbourne, Vic. 3010, Australia

a r t i c l e i n f o

Article history:Received 29 February 2012Received in revised form 16 May 2012Accepted 25 May 2012Available online 6 June 2012

Keywords:Electron tomographyDenoisingPlasmodiumNon-linear anisotropic diffusion filtering

1047-8477/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.jsb.2012.05.019

Abbreviations: NAD, non-linear anisotropic diffudiffusion; CED, coherence enhancing diffusion; EMfiltered back projection.⇑ Corresponding authors. Postal address: Depar

Molecular Biology, Bio21 Institute, The University oRoad, Melbourne, VIC 3010, Australia. Fax: +61 38344

E-mail addresses: edmundak@unimelb.edu.auunimelb.edu.au (H. Quiney), ltilley@unimelb.edu.au (

a b s t r a c t

Electron tomography produces highly magnified 3D image volumes useful for investigating the structureand function of cellular components. Image quality is degraded by multiple scattering events and quan-tum noise, which depend on the angle at which individual tilt projections are collected. We have adapteda biomedical imaging approach to improve image quality by enhancing individual tilt projections prior tovolumetric reconstruction. Specifically, we have developed a family of non-linear anisotropic diffusion(NAD) filters parameterized by the tilt angle. We give a quantitative and qualitative evaluation of ourpre-processing approach and the NAD filter. We show an improvement in the reconstructed volumesfor tomograms generated from both plastic-embedded and cryo-stabilized samples of malaria parasite-infected erythrocytes.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Electron tomography is an important technique that is used toelucidate the 3D architecture of biological samples (Downinget al., 2007; Leis et al., 2008; Milne and Subramaniam, 2009; Van-hecke et al., 2011). The method involves generating sections ofcells or tissues (usually 200 – 400 nm) and preparing the samplesfor electron microscopy (EM). Samples can be processed using typ-ical EM protocols involving chemical fixation, plastic embedding,sectioning, and staining with heavy metals (Frey et al., 2006; Ganand Jensen, 2012; McIntosh et al., 2005). Alternatively samplescan be snap frozen in vitreous ice, optionally sectioned and exam-ined using a cryo-EM stage (Pierson et al., 2011; Tocheva et al.,

ll rights reserved.

sion; EED, edge enhancing, electron microscopy; FBP,

tment of Biochemistry andf Melbourne, 30 Flemington1421.

(E. Kazmierczak), quiney@L. Tilley).

2010). Ultrarapid freezing permits a marked improvement in thepreservation of cellular structures in their native state; howeverunstained vitreous samples have rather low intrinsic contrast(Dubochet et al., 1988; McDonald and Auer, 2006). A third possibil-ity is high pressure freezing followed by freeze-substitution andresin-embedding. This helps preserve cell structure but also per-mits the enhancement of sub-cellular features by contrasting withmetal stains. Once the sections have been prepared they are exam-ined in an electron microscope with a tiltable stage operating atmoderate electron accelerating voltages (200–400 keV). Images ofthe sample are collected over a tilt range of at least 120�. The imag-ing dose is kept as low as possible (and for cryo-stabilized samplesshould not exceed 10,000 e�/nm2) in an effort to preserve the bio-logical structures. The images are aligned, usually making use ofcolloidal gold fiducial particles that are deposited into the sample(Kremer et al., 1996; Mastronarde, 1997; Penczek et al., 1995).The final volume, or tomogram, is obtained through a computa-tional volumetric reconstruction process (Herman, 2009) andprocessed using different segmentation tools (Ali et al., 2012;Kremer et al., 1996; Mumcuoglu et al., 2012; Nguyen and Ji,2008). The reconstructed volume is commonly post-processed to

M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142 133

improve the image by enhancing features of interest such asboundaries and regions of similar image density. This is done spe-cifically to facilitate segmenting objects of interest.

The quality of the electron microcopy projection images isdetermined by factors that affect the mean free path of the elec-trons as they pass through the specimen. A major determinant isthe thickness of the sample, a parameter that varies non-linearlyas the section is tilted. For example the sample is approximatelytwo times thicker at an angle of 60� and three times thicker at70� (Grunewald et al., 2003; Lucic et al., 2005; Steven and Aebi,2003). Thus, multiple scattering events increase markedly at high-er tilt projection angles. This contributes to what is referred to asnoise in the reconstructed tomogram (Frangakis and Hegerl,2001). Where the appropriate hardware is available, energy filter-ing can be used to remove a significant portion of inelastically scat-tered electrons, which improves contrast and the signal-to-noiseratio (Mastronarde, 2005). Energy filters have been found to bevaluable for improving imaging of both stained plastic sections(Bouwer et al., 2004; Han et al., 1996) and frozen-hydrated speci-mens (Grimm et al., 1997; Koster et al., 1997).

In cryo-electron tomography on cryo ultrathin sections (Al-Amoudi et al., 2004; Hoenger and Bouchet-Marquis, 2011; Hurbainand Sachse, 2011) or macromolecules embedded into thin layers ofvitrified ice (Dudkina et al., 2011), multiple scattering is less of aproblem, but quantum noise remains a problem due to insufficientsampling of the electron scattering from the specimen. Signal aver-aging is not possible due to the variability in the size and shape ofcellular structures. Degradation of the signal can also arise due toinstrument defects such as imperfections of the CCD cameras.The signal obtained at higher angles is particularly weak, and sub-ject to the inherent granularity of Poisson counting statistics.

Noise-related artifacts are an important issue in electrontomography and can severely compromise the quality of the recon-structed volume (Baumeister et al., 1999). Improving the quality ofthe reconstructed tomogram would help elucidate important bio-logical structures and facilitate further processing, such as segmen-tation and rendering. Indeed the impressive results obtained byelectron crystallography (Fujiyoshi, 1998) and single particle anal-ysis (Frank, 2002) are attributed to ‘‘noise’’ reduction strategies,that rely on image averaging (Bartesaghi and Subramaniam,2009; Frangakis and Hegerl, 2001; Hegerl and Frangakis, 2006).

Non-linear anisotropic diffusion (NAD) is a generic, establishedstatistical method (Perona and Malik, 1990; Weickert, 1999) thatcan be interpreted in terms of scale space theory (Koenderink,1984; Lindeberg, 1992) and which can be used for volumetricdenoising of reconstructed tomograms (Narasimha et al., 2008).Popular NAD filters for local enhancement are based on edgeenhancing diffusion (EED) and coherence enhancing diffusion(CED) methods (Weickert, 1999). The successful application ofNAD to noise reduction in X-ray computed tomography sinogramsfor medical imaging (Alrefaya et al., 2009; Demirkaya, 2001; Liet al., 2004; Wang et al., 2005; Zhou et al., 2007) suggests potentialbenefits from applying similar methods to EM tilt projections.

The first hybrid approach for the local enhancement of 3D fea-tures of electron tomography reconstructed volume was developedby Frangakis and Hegerl (2001). An enhanced image was obtainedby the alternation of EED and CED filters triggered by a discreteswitch. Some variations of the discrete switch approach have alsobeen presented (Fernandez and Li, 2003, 2005). A continuousswitch function that combines EED and CED was applied to com-puted tomography volumes (Mendrik et al., 2009). The switchdid not, however, take into account the local gradient of the imageat different tilt angles.

The noise in EM projection data varies with the tilt angle,decreasing the quality of the reconstructed electron tomogram.As a result, post-reconstruction correction might not be sufficient

to obtain a clear, artifact-minimized volume for very noisy tomo-grams. The use of additional iterations of the post-reconstructionmanipulation may result in cleaner images but at the price of lowercorrelation with the original dataset (Bazán et al., 2009). Applica-tion of a filtering procedure to two-dimensional electron micro-scope images before they are assembled to form a three-dimensional tomographic representation provides a method forcustomizing the filtering process based on the quality of the pro-jection image data at different angles.

A crucial question is when to stop the filtering process (i.e. theoptimal number of iterations), so that the signal information is notmisclassified or blurred out. Several objective stopping criteriahave been proposed (Mrazek and Navara, 2003), but most of themare not suitable for cryo-electron tomography data (Fernandez andLi, 2003). The noise-estimate variance introduced by Fernandezand Li, (2005) seems to provide statistical criteria that are best sui-ted to electron tomography data. Unfortunately, a uniform regionhas to be manually selected by a user, which makes the outcomedependent on a subjective judgement regarding how the regionis selected within a specific image.

Statistical analysis and manipulation of the individual tilt pro-jection images can be used to optimize the reconstruction process.Statistical iterative reconstruction, rather than the classic filteredback-projection (FBP) with low-pass filtering, is one way to dealwith the problem (den Dekker et al., 2005; Elbakri and Fessler,2002, 2003; Whiting, 2002). Another possibility is to use statis-tics-driven processing (in general) and non-linear anisotropic dif-fusion (in particular) to obtain a noise-reduced sinogram thatwill satisfy the FBP reconstruction for the Radon transform (Alre-faya et al., 2009; Demirkaya, 2001; Li et al., 2004; Wang et al.,2005; Zhou et al., 2007). The benefits of the latter include a highercomputational efficiency and more uniform spatial resolution inthe reconstructed image. To our knowledge NAD has not previ-ously been successfully applied to electron tomography tiltprojections.

In this paper we present a method for applying an angle-depen-dent NAD filter (referred to as pre-NAD) to individual projectionimages before reconstruction. This involves scaling the informationfor each tilt image to allow for the effect of the altered geometry ofthe samples at higher angles. We use a stopping criterion for iter-ations in the pre-NAD filter based on masked variance differenceand show that our pipeline can overcome problems associatedwith a lack of continuity of information observed with multiple2D tilt projection denoising approaches (Frangakis and Hegerl,2001). We show examples where the method is applied to EMdata collected under sub-optimal imaging conditions. We haveexamined fixed and stained sections as well as cryo-stabilizedsections.

2. Materials and methods

2.1. Electron tomography

Plasmodium falciparum-infected RBCs were cultured, harvested,fixed, dehydrated, embedded with resin, and sectioned (200 nm) aspreviously described (Hanssen et al., 2010). The sections werestained with uranyl acetate and lead citrate, layered with gold fidu-cials and observed on a Tecnai G2 F30 (FEI Company) transmissionelectron microscope at 300 keV (Bio21 Institute, Melbourne). Forelectron tomography, tilt series projections were acquired usingXplore 3D (FEI Company) (Abu Bakar et al., 2010; Hanssen et al.,2008) and aligned using the IMOD package (Kremer et al., 1996)on a Ultrascan 1000 (Gatan, Pleasanton, CA, USA) 2k�2k camera,and binned by a factor of 4. For high quality ‘‘ground truth’’ data,tilt projections were acquired at 1.5� intervals between -70� and

134 M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142

+70�, using a 1 s exposure time. For test data we used both a lowerexposure time (0.2 s) and a larger tilt interval (3�) to enhance noiseand artifacts and degrade the signal.

2.2. Cryo EM methods

P. berghei sporozoites were isolated from midgut of a mosquitoand cryo stabilized as described previously (Kudryashev et al.,2010). Tomography was performed on a CM300 microscope (FEI)operated at an accelerating voltage of 300 keV, equipped withGatan Imaging Filter with a slit of 20 eV. Tilt series were acquiredbetween �60 and +60� with 2� step with the total dose of electronskept below 10,000 e�/nm2, with objective lens under-focus of12 lm. Tilt series alignment and reconstruction was performedusing the IMOD package, aided by 10 nm gold beads (Kremeret al., 1996).

2.3. Image analysis

The test tilt projections were automatically aligned one-by-oneto the ground truth projection. Following application of our filter tothe tilt projection data, tomograms were reconstructed using Fil-tered Back Projection (FBP). No post-processing was applied.

For a visual assessment, we performed semi-automatic segmen-tation and 3D rendering. A threshold value was selected manuallyfrom each reconstructed tomogram using a noise-estimate vari-ance criterion, after marking some of the relevant cellular features,as described by others (Fernandez and Li, (2005). Connected re-gions were identified automatically using connected componentanalysis (Ibanez et al., 2003). The automatic segmentation algo-rithm is described in Appendix I. The regions were labeled with dif-ferent colors, and 3D models were generated and rendered(Yushkevich et al., 2006).

2.4. Simulation

A synthetic volume of dimensions 256 � 256 � 60 voxels wascreated in MATLAB (Mathworks� Natick, MA, USA).

The double membrane was simulated as a ‘‘Mexican hat’’ usingthe two 3D sinc functions:

sinðxÞ=x; x 2 R3

and

10þ sinðxÞ=x; x 2 R3

Projections of the synthetic volume were obtained at angles of�70� to +70�, with a 2� increment for each projection, using Xmipp(Sorzano et al., 2004). The final volumes were reconstructed andsegmented. Reconstructions were performed using tomo3d(Agulleiro and Fernandez, 2011). Segmentations were performedusing a scale space approach, as explained in Appendix I. Renderingwas performed using ITK-snap (Yushkevich et al., 2006).

2.5. Diffusion filtering

The grayscale intensity, I, of each image is regarded as a densitythat is redistributed by a conservative diffusive process. The equil-ibration of intensity due to its inhomogeneity is determined byFick’s law of diffusion, so the time-evolution of I is obtained bysolving the diffusion equation:

@I@t¼ r � ðDrIÞ

where D is the diffusion tensor. If it can be assumed that D is con-stant over the entire domain of I, the diffusion process is described

as homogeneous and if it depends only on position it is described ashomogeneous. Here, however, it is assumed that D depends on thelocal nature of the time evolution of I and the diffusion process thatdefines the filtering procedure is consequently described as non-lin-ear, inhomogeneous and anisotropic.

The prototype non-linear diffusion filter (Malik and Perona,1990) employed an isotropic model of the form D = g(rI�rI)I,where I is the unit tensor of appropriate dimensionality andg(s2) = (1 + s2/l2)�1 in which l is a real, positive parameter. The po-sitive-definite character of D enables one to generalize this ap-proach to the case of anisotropic non-linear filtering by writing,in two dimensions,

D ¼vT

1

vT2

" #k1 00 k2

� �v1 v2½ �;

where v1 and v2 are orthonormal column vectors that specify theprincipal axes of the anisotropic diffusion tensor and k1 and k2 arescalar functions of the local image gradient. Generally, these ortho-normal vectors are selected at each location in the image to coincidewith the eigenvectors of J0 which is defined by the outer product ofthe intensity gradient,

J0 ¼ rI � rIT :

The components of the intensity gradient are approximated by thecentral difference formula. More generally, one may adopt eigen-vectors derived from Jr ¼ J0 � Kr, which represents the convolutionof J0 with a Gaussian function of width r. The solution of the matrixeigenvalue equation for J0 or Jr determines two eigenvalues, l1 andl2, that may be used to quantify the local anisotropy of I, for whichpurpose we adopt the convention that l1 P l2. The diagonalizationof Jr generates a unitary rotation on an orthonormal basis of Carte-sian unit vectors that may be used to align the diffusion tensoralong the principal directions of intensity change. Having specifiedv1 and v2 which become, respectively, the major and minor axes ofD, one then has the freedom to control the magnitude of the localdiffusion characteristics by allocating real, non-negative numericalvalues to k1 and k2.

The magnitude of r that is used to define the Gaussian convolu-tion function Kr determines the spatial interval over which thestructure tensor is calculated (Babaud et al., 1986; Koenderink,1984; Nielsen et al., 1997). Small values of r generates a narrowspatial Gaussian distribution which causes negligible smoothingof the image. Large values of r smooth out noise but may obscuresignificant features, such as edges and discontinuities. The pro-jected depth through the sample, which is assumed to be a thinslab, clearly depends on the tilt angle, / which is measured be-tween the electron beam direction and a vector perpendicular tothe slab. As a consequence, the smoothing parameter must dependon the tilt angle, for which purpose we have adopted the relation r(/) = r0cos(/), where r0 is the value of r chosen in the case wherethe incident beam is perpendicular to the slab. In the limit / ? p/2the projected length traversed by the beam becomes large com-pared to the thickness of the slab and r(/) ? 0, indicating thatno smoothing is to be performed and no small details are to be ob-scured by the convolution process. The decreasing magnitude ofr(u) for increasing / reduces, as a consequence, the spatial inter-val over which rI must be calculated in the determination of Jr.

The non-linear anisotropic diffusion (NAD) algorithm of Franga-kis and Hegerl (2001) is a hybrid of the edge enhancing diffusion(EED) method, which enhances changes in image intensity, andthe coherence enhancing diffusion (CED) method (Weickert,1999), which enhances regions that exhibit correlations in imageintensity. Here, the NAD approach is modified to incorporate r-dependence in the determination of the principal axes of D fortwo-dimensional tilt projections. The hybrid NAD algorithm

M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142 135

employs the EED method if l1 � l2 P tg for some user definedthreshold, tg, which controls the detection of edges in the image.If this inequality is not satisfied, the CED method is adopted. Themodification of the EED and CED algorithms to include dependenceon the tilt angle both require the calculation of the eigenvectors ofJr(/), which define the principal axes of D for a given /.

The EED and CED algorithms differ primarily in their specifica-tions of k1 and k2, which are used to construct D to smooth twodimensional images obtained at fixed /. For the EED algorithm,these parameters are defined by,

ke1 ¼1 if Gðr/Þ ¼ 0

1� exp �c Gðr/Þ4

W

� �h iif Gðr/Þ > 0

8<:

ke2 ¼ 1

where Gðr/Þ ¼ rIr/� rIr/

, C = 3.31488 is a threshold parameteradopted from Mendrik et al. (2009) and W ¼ k2

e , where ke = 30 is auser-specified parameter defined by Weichert (1996) and Weichert(1999). For the CED algorithm, the corresponding parameters arechosen to be,

kc1 ð/Þ ¼ a

kc2 ð/Þ ¼1 ifl2 ¼ 0

aþ ð1� aÞ exp � logð2Þ�k2c

Kð/Þ

� �otherwise

(

where kc is another user-defined parameter whose value is typicallyset to kc, = 30, a = 0.001,

Kð/Þ ¼ l1ð/Þaþ l2ð/Þ

� �

and the parameters l1(/) and l2(/) are the eigenvalues of Jr(/).A straightforward generalization of the hybrid NAD approach to

arbitrary tilt angles would swap discontinuously between the EEDand CED algorithms based solely on the value of l1(/) � l2(/).Instead, we have developed a continuous switch between EEDand CED based on Mendrik’s parameterization of the diagonalterms in the diffusion tensor,

kið/Þ ¼ ð1� eð/ÞÞkcið/Þ þ eð/Þkei

ð/Þ;

where i = 1, 2. The tilt-dependent parameter, e(/), is defined by,

eð/Þ ¼ e

eþ exp �ðnð/Þ�n̂ð/ÞÞkið/Þ

h iwhere

nð/Þ ¼ 4 logð1þ aþ l1ð/Þ � l2ð/ÞÞ þ 4 log 1þ aþ l1ð/Þaþ l2ð/Þ

� �;

n̂ð/Þ is the mean value of n(/) taken over all pixels for tilt angle /and a is a small, real, positive regulating parameter. The limitn(/) = 0 corresponds to the presence of an edge and the EEDalgorithm is favored in the choice of e(/). Otherwise, a progressivelylarger contribution from the CED algorithm in included in ourtilt-dependent hybrid approach. Finally, we have constructed atilt-parameterized representation of the diffusion tensor,

Dð/Þ ¼vT

1ð/ÞvT

2ð/Þ

" #k1ð/Þ 0

0 k2ð/Þ

� �v1ð/Þ v2ð/Þ½ �:

The specification of the principal axes of D(/), v1(/) and v2(/)defines two independent, orthogonal directions of diffusion withmagnitudes k1ð/Þ and k2ð/Þ;, respectively. Both the directionsand magnitudes are parameterized with respect to the tilt angle,

and the magnitudes are further parameterized to accommodate acontinuous transition between regions in which there are edgesand regions in which the image is smooth.

In our approach, anisotropic filtering is applied using this con-tinuously parameterized hybrid approach to each tilt projectionimage before tomographic reconstruction is performed. Featuresin each tilt projection may be difficult to identify, however, be-cause of the dependence of the electron path-length through thesample as a function of /. As a consequence, anisotropic filteringof the tilt images is performed iteratively until either (1) self-con-sistency has been obtained in the reconstructed image or (2) a pre-determined number of iterations has been reached.

The self-consistency criterion is based on the weighted varianceof the reconstructed image compared to the measured values. Inorder to control the amount of smoothing that is applied to the im-age, pixels are excluded from the calculation of the variance if theyare likely to correspond to edges, which are identified if theinequality n̂ð/Þ < nð/Þ is satisfied. A binary mask, fi, is constructedfor each pixel, i. If the pixel is judged to contain an edge, then fi, = 0;otherwise, fi, = 1. The masked variance difference, d, is defined to be

d ¼ var½fiðIti � I0

i Þ�;

where Iti is the value of the image at the pixel labeled i after t iter-

ations and I0i represents the corresponding measured values. The

mask restores the conventional definition of the variance to includeall values of i in the image. The iterative refinement of the tiltimages proceeds until d < dstop, where dstop is specified by the userin a manner similar to that described by other groups (Fernandezand Li, 2005). The maximum noise variance, dstop, was estimatedfrom one of the highest tilt angle projections, by the followingmethod. The pre-NAD filter is iterated until the relative difference,(di+1 � di)/di is 0.05 or less, and then dstop is defined to be di+1. Thisprocedure results in a variation in the number of iterations usedfor each projection. We found that the number of iterations wasapproximately linearly correlated with the cosine of the tilt angle.

3. Results

Electron tomograms are generated from projection images col-lected at different tilt angles. The apparent thickness of the samplevaries non-linearly as the section is tilted with resultant variationsin the mean electron path and anticipated degradation in the qual-ity of the images at high tilt angles. When a tomogram is generatedfrom a data set that includes images with a low signal-to-noise ra-tio, faithful isosurface representation and volume rendering maybe problematic.

In an effort to improve the quality of electron tomography datawe have designed an approach that uses NAD filtering before vol-ume reconstruction. For a simple visual impression the approachwas applied to a 2D test image (photo of Marie Curie), whichwas degraded by addition of Gaussian noise (Fig. 1A). The degradedimage was subjected to isotropic and median filters, or to pre-NADprocessing. The masked variance difference increases with increas-ing iterations (Fig. 1B).

We have assessed the usefulness of our approach using a simu-lated model. A synthetic volume was created using MATLAB andconsists of two regions, one simulating a double membrane andthe other the cell cytoplasm. Electron density values for the two re-gions were randomly picked in the ranges 600–850 and 750–900,respectively (Fig. 2A). Projections of the synthetic volume weresimulated at angles of �70� to +70� (Sorzano et al., 2004) and thefinal volumes was reconstructed (Agulleiro and Fernandez, 2011)and segmented (see Appendix I). As shown in Fig. 2B, very littlestructural information is retrieved from the unprocessed data (firstcolumn). A traditional post-reconstruction NAD approach (second

Fig. 1. Analysis of noise reduction by NAD filtering using masked variance difference. (A) A test image ‘‘Marie Curie’’ (193 � 241 pixels) (a) was degraded with Gaussian noise(standard deviation = 25) (b), and the degraded image was subjected to isotropic and median filters (c and d) or to pre-NAD-processing for 2–8 iterations; ke = kc = kh = 30,r = 1, a = 0.001, maximum noise variance = 0.053. (B) Monotonically increasing behavior of masked variance difference at different numbers of iterations.

136 M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142

column) improves the analysis but our pre-NAD approach (thirdcolumn) or a combination of traditional approach with our pre-NAD (fourth column), shows a marked improvement. For this com-parison the number of iterations used for the post-reconstructionNAD approach was chosen to be equivalent to the average numberof iterations used for the pre-NAD approach.

It is likely that reconstructions using the unprocessed and tradi-tional NAD approaches are more sensitive to missing wedge arti-facts than our pre-NAD approach. It is also possible that our non-linear pre-filtering approach, which reduces noise and enhancesedges, could enhance some boundaries and suppress others, creat-ing some anisotropy in the reconstruction.

In an effort to assess the success of the different approaches wehave computed the distance between the obtained and the ex-pected segmentation data using Hausdorff symmetric distance,measured in pixels (Gerig et al., 2001). For the unprocessed datawe obtained 149, for the traditional NAD processed data, 103,while for the pre-NAD processed data, 82. A slightly better result(78) was obtained from application of the pre-NAD filter beforereconstruction and traditional NAD after reconstruction.

We have also assessed the usefulness of our approach usingtransmission EM images of P. falciparum-infected RBCs collectedunder different conditions. To generate these data parasite-in-fected RBCs were harvested, fixed and prepared for embedding.Sections (200 nm) were stained with uranyl acetate and lead cit-rate, then layered with gold fiducials as described previously(Abu Bakar et al., 2010; Hanssen et al., 2008). A high quality‘‘ground truth’’ data set was collected by recording tilt images be-tween �70� and +70� at 1.5� intervals, using a 1 s exposure time.The data were aligned using IMOD and binned by a factor of 3.Some of the projection images at different tilt angles are presented(Fig. 3i). An additional tilt series of the same specimen was ac-quired at a lower exposure time (0.2 s) (Fig. 3ii). The degradationof the data and the appearance of instrument noise are evident.Application of the pre-NAD filtering algorithm significantly im-proved the quality of the data (compare Fig. 3i–iii).

The tilt images for the high quality data set were aligned withIMOD and a tomogram was reconstructed using FBP (Fig. 4A). Ina virtual section from the tomogram, a pair of electron-dense rhop-try organelles (marked R1 and R2) is observed at the apical end of

Fig. 2. Application of pre-NAD filtering to a test object. (A) A synthetic volume was created simulating a double membrane in the cell cytoplasm. (B) Projections of thesynthetic volume were generated with pre or post filtering and the final volumes were reconstructed and segmented. Row (i) shows a view of the volume, row (ii) the volumewith segmentation superimposed, and row (iii) the 3D rendering of the segmented simulated membrane. The parameters used for post-NAD were k = 30, 6 iterations, andr = 0.5. The parameters used for pre-NAD were maximum noise variance (dstop) = 0.7, maximum number of iterations = 15, ke = kc = kh = 30. The number of iterations (from 3 to15; average of 6 (standard deviation 2.5)) varied in an approximately linear fashion with the projection angle, with a strong correlation between the number of iterations andthe cosine of the tilt angle (Pearson’s correlation values of q = 0.63, p = 5 � 10�9). The parameters for the automatic segmentation were n = 5, r = 1.0, t = 1/(n�1) = 0.25.

Fig. 3. Application of pre-NAD filtering to electron micrograph projection images collected at different angles. EM transmission projection images collected at angles from�70o to +70o of a stained fixed section (200 nm) of a P. falciparum-infected RBC. A high exposure ‘‘ground truth’’ data set (i; 1 s exposure) and a low exposure ‘‘test’’ data set (ii;0.2 s) were collected. The low exposure data set was filtered using the pre-NAD algorithm (iii).

M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142 137

Fig. 4. Improvement in electron tomogram reconstruction following application of pre-NAD filtering to a limited angle data set. A high exposure ‘‘ground truth’’ data set (A;1.0 s exposure, 1.5� interval) and a low exposure ‘‘test’’ data set (B; 0.2 s exposure, 3� interval) were collected. Reconstructions were performed using the FBP approach usingtomo3d (Agulleiro and Fernandez, 2011). Low (i) and higher (ii) magnification images are presented. Scale bars: 200 nm. The low exposure data set was filtered using thepost-reconstruction NAD filter of Frangakis (C) or the pre-NAD algorithm (D), or both pre- and post-NAD filtering (E). The RBC cytoplasm (RBC), two rhoptry organelles (R1 andR2), the merozoite apical end (M), and the peripheries of two nuclei (n) are marked. The parameters used for post-NAD were k = 30, 6 iterations, and r = 4.1 nm. The pre-NADfilter parameters were: ke = kc = kh = 30, r = 4.1 nm, maximum noise variance (dstop) = 0.08, maximum number of iterations = 10, a = 0.001. The number of iterations varied in anapproximately linear fashion with the projection angle from 3 to 10 with an average of 6 iterations (standard deviation 1.1). All the aligned tilt projections have been down-sampled (bin = 4). The graphs (iii) show analyses of the intensity variations across the data in the region of the line. A low electron-density region between the rhoptries (c), aregion at the edge of rhoptry 1 (d) and region within rhoptry 2 (e) are indicated. (iv,v) Low and high magnification views of the reconstructed volumes that have been semi-automatically segmented and rendered. Automatic segmentation was achieved as described in Appendix I.

138 M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142

the daughter merozoite (M), which is developing within a motherparasite. The tilt projection images for the lower exposure datawere automatically aligned to the equivalent ground truth dataset. Due to the extremely low quality of the test data and the dif-ferent grayscale values, the normalized mutual-information dis-tance metric (Pluim et al., 2003) was preferred over both cross-correlation and manual alignment. We applied our filter to thepoor quality tilt projections before the data were reconstructedusing FBP. There is no substantial difference whether reconstruc-tions were performed using the FBP method (shown) or the Simul-taneous Iterative Reconstruction Technique (SIRT) method (notshown). The improvement in the quality of the data upon applica-tion of the pre-NAD filtering algorithm is evident from visualexamination of the reconstructed tomograms (compare Fig. 4B-iiand D-ii). For comparison we also applied a post-reconstructionNAD filtering algorithm (Frangakis and Hegerl, 2001) (Fig. 4C)and both pre- and post-processing (Fig. 4E).

An analysis of the intensity variations across the tomogram inthe region of the line (Row iii) shows the improvement with thedifferent filtering methods. The ground truth profile (column A)clearly shows the boundary between the two rhoptry organelles(R1 and R2) as an electron lucent region (high gray values) indi-cated by the aqua arrow (c) that separates two electron-dense re-gions (lower gray values). Each of the filtered low exposure

reconstructions (columns C–E) shows a clear electron-dense edge(low gray values) at the boundary of rhoptry R1 (i.e. under thered arrow), which is less well defined in the unfiltered reconstruc-tion (B). For example, the unfiltered tomogram contains a feature(marked with red arrow (d)) that is not present in the ground truthtomogram. This feature is partially removed by post-filtering (C)and more effectively removed by pre-filtering (D and E). The pre-NAD filtered reconstructions (D and E) also more faithfully returnthe more homogenous staining profile of the adjacent rhoptry(marked with green arrows (e)) than the post-NAD filtered recon-struction (C).

We performed semi-automatic segmentation and 3D renderingof the data (Fig. 4iv and v). Connected regions were automaticallyidentified using scale space analysis and Otsu thresholding (SeeAppendix I), then 3D modeled and rendered (Yushkevich et al.,2006). In the reconstruction from the high quality data, a numberof features are detected (Fig. 4A-iv and v). A very similar set of fea-tures was detected when the pre-NAD filtering algorithm was theapplied to the low quality data set (Fig. 4D and E-iv, v). By contrast,when the lower quality data was reconstructed without pre-pro-cessing only very minimal cellular information is retrieved(Fig. 4B-iv and v). The improvement obtained using pre-NAD filter-ing that is apparent by visual inspection is confirmed by computingthe distance between the obtained and the expected segmentation

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data using Hausdorff symmetric distance. For the unprocessed datawe obtained 122, for the traditional NAD processed data, 63, for thepre-NAD processed, 48, and for the combination of traditional NADand pre-NAD, 49.

As a further test we examined electron tomography data col-lected from a low contrast sample (Fig. 5). P. falciparum-infectederythrocytes in the early stages of schizogony (cell division) werefixed and sectioned (200 nm) and stained with uranyl acetate butno lead citrate. A series of tilt projections was collected and tomo-grams were constructed with and without pre-NAD filtering. In avirtual section from the unprocessed tomogram (Fig. 5A; detail inC) cellular features are difficult to distinguish. The contrast is im-proved in the virtual section from the tomogram generated afteranisotropic smoothing of the tilt projections (Fig. 5B and D). Inthe data from the improved tomogram (Fig. 5D), electron denserhoptries (R) are evident near the apical end of one of the develop-ing daughter cells. The uppermost rhoptry organelle is very

Fig. 5. Application of pre-NAD filtering to poor contrast EM data. A fixed section of a P. faA tilt series was collected and tomograms were constructed without (A and C) and wr = 13.7 nm, maximum noise variance (dstop) = 0.0078, maximum number of iterations = 20, athe electron dense rhoptries (R) and an apical prominence (a) are marked. The intensity p(F) Automatic segmentation was achieved as described in Appendix I.

difficult to discern in the unprocessed data but readily distin-guished in the processed data. Similarly, an apical prominence(a) is hard to discern in the unprocessed data but more evidentin the processed data. The improvement is also evident in theintensity variations across the tomograms in the region of the line(Fig. 5E). We performed a fully automatic segmentation and 3Drendering (see Appendix I) of the data (Fig. 5F). A number of impor-tant features are identified.

Unstained vitreous sections imaged by cryo EM have low intrin-sic contrast, and could benefit from the application of the pre-NADfiltering algorithm. We generated a data set for an entire unsec-tioned �400 nm thick P. berghei sporozoite that was shock-frozenand prepared for cryo EM (Kudryashev et al., 2010) (Fig. 6). Thesedata were collected with electron filtering but similar results wereobtained for data collected without electron filtering (not shown).

Tomograms were generated without (Fig. 6A and C) and with(Fig. 6B and D) application of the filtering algorithm prior to

lciparum-infected erythrocyte was subjected to a staining with uranyl acetate alone.ith (B, and D) pre-NAD filtering. Scale bar: 300 nm. Parameters: ke = kc = kh = 30,= 0.001. The RBC membrane (RBC), the parasite surface (P), hemozoin crystals (Hz),

rofiles of the yellow lines in (C) and (D) are depicted in (E) (top and bottom panels).

Fig. 6. Application of pre-NAD filtering to cryo EM analysis of a P. berghei sporozoite. P. berghei sporozoites were shock frozen and prepared for cryo EM. The region displayedrepresents the apical end of the parasite, presented as a slice projection through a tomogram. (A) Unprocessed tomogram. (B) Tomogram generated using pre-NAD filtering.Parameters: ke = kc = kh = 30, r = 8.2 nm, maximum noise variance (dstop) = 0.0019, maximum number of iterations = 15, a = 0.001. (C and D) Detail of (A) and (B). The intensityprofiles across the yellow lines in (C) and (D) are depicted in (E) (top and bottom panels). (F–H) Rendering of features in the tomograms illustrating the detection of theparasite surface (red), the inner membrane complex (blue), and two layers of microtubules (pink). Automatic segmentation was achieved as described in Appendix I. Scalebars: 150 nm.

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generation of the tomograms. Analysis of individual sections fromthe 3D reconstructions reveals a substantive improvement in thequality of the data. This is evident in the variation in the gray levelsalong lines through the data sets (Fig. 6E). Features in the recon-structed tomogram were identified using fully automatic segmen-tation and 3D rendering (Fig. 6F–H). The surface of the parasite wasreadily detected (red), along with the underlying inner membranecomplex (blue). We observed two layers of microtubules (pink).These features are more difficult to detect in the raw tomogram

data. For example, the red and green arrows in (E) point to theRBC membrane and the second row of microtubules; these featuresare very difficult to distinguish without pre-NAD filtering.

4. Discussion

Diffusion filtering is often used to smooth or restore noisyimages. The formulation of such partial differential equation filter-ing schemes is based on the observation that an image locally

M. Maiorca et al. / Journal of Structural Biology 180 (2012) 132–142 141

resembles a fluid flow pattern that may be recognized as a signif-icant feature, as it might be either a boundary or a homogeneousregion of the image. The target image is, in effect, regularizedand modeled as a physical, diffusive system that evolves from aninitial state specified by the original noisy image into a successionof smoother states. This evolution may be regarded as a scalespace, in which the original image is embedded into a hierarchyof images in which detail is visible on variable length scales. Anextension of this approach was proposed (Perona and Malik,1990), in which a non-linear diffusion filtering scheme utilizedinformation about the gradients of the evolving images to controltheir diffusion characteristics and to detect and enhance edges.

NAD filters have been in use for some years for post-reconstruc-tion denoising of tomograms. There is, however, a potential prob-lem with this approach, when applied to electron tomograms,which are generated from a series of projection images at differenttilt angles. In these data sets the signal to noise ratio varies withthe tilt angle, and the data at very high angles (>70o) cannot be col-lected, resulting in the so-called ‘‘missing wedge’’ of information.Furthermore, the reconstructed electron tomogram is potentiallyaffected by a range of reconstruction artifacts. The application ofpost-reconstruction NAD filtering may exacerbate these artifacts.Here, we extend the general NAD filtering approach by applyingthe diffusive filtering procedure to two-dimensional electronmicroscope images before they are assembled to form a three-dimensional tomographic representation.

We have applied a scale space approach to compensate for theincreasing amount of information per pixel in each tilt projection,which is linked to the increased mean free path length of electronswithin the sample at different tilt angles. This permits better dis-tinction between boundary and homogeneous regions, allowingaccurate denoising of each tilt projection before reconstruction,thus allowing better visualization and rendering of the recon-structed tomogram.

Tomographic reconstruction processes usually assume a linearrelationship between the projection image intensity values andthe object density values. We have instead assumed that the diffu-sion tensor depends on the local nature of the time evolution of thetilt projection image; the diffusion process that defines the filteringprocedure is consequently described as non-linear, inhomoge-neous and anisotropic. We have shown that the careful treatmentof the non-linearities in each tilt projection greatly facilitates thesubsequent tomographic reconstruction of the volume using theNAD approach.

There is a potential problem due to superimposition of featuresin the projection images, which might exacerbate the employmentof a pre-filtering approach. We have attempted to ameliorate thiseffect by selecting the parameters that control the diffusion pro-cess using a continuous discriminator for edges and homogeneousregions without anticipating what the structures should look like,as for conventional 3D post-reconstruction approaches.

In our approach the masked variance difference value, d, is de-fined by the user in an approach similar to that employed by othergroups (Fernandez and Li, 2005). This gives the user the flexibilityto vary the process depending of specimen characteristics throughthe use of a mask function to exclude the likely positions of edgesfrom the smoothing procedure. The termination of the iterations ofthe algorithm is ensured by its monotonically increasing behaviorand by setting a maximum number of iterations. Further work todevelop an automatic process for detecting the variance differencethreshold may be desirable.

In summary, we provide a method for noise reduction with sig-nal preservation by denoising 2D projection images before recon-structing 3D images. It is faster than post-reconstructionprocessing, and while all filtering approaches have the potentialto introduce artifacts, the pre-filtering approach is designed to

minimize artifacts due to contribution of the degraded signal fromhigh tilt data in the reconstructed volume. We have applied themethod to EM images of malaria parasite-infected RBCs. We findthat features can be retrieved from data collected under sub-opti-mal imaging conditions (i.e. low-dose or low-staining or thickspecimens). The method provides improvements in tomogramquality for both fixed, stained sections and cryo-stabilized sections(with or without energy filtering). Filtering techniques are used tooptimize data obtained from a range of X-ray- and electron-basedimaging methods. Pre-reconstruction filtering techniques may alsoprove useful in other tomographic imaging applications.

Acknowledgments

The authors acknowledge support from the Australian ResearchCouncil and the Australian National Health and Medical ResearchCouncil. We thank Kenneth Downing, Lawrence Berkeley Laborato-ries, CA, USA and Carlos Oscar Sorzano, Centro NacionalBiotecnología, Madrid, Spain, and Bernard Heymann, NationalInstitutes of Health, MD, USA, and David Mastronarde, Universityof Colorado, CO, USA, and Ruben Dilanian, University of Melbourne,Australia, for helpful discussions. We thank Freddy Frischknechtand Marek Cyrklaff (University of Heidelberg, Germany) and Wolf-gang Baumeister (Max Planck for Biochemistry, Munich, Germany)for support in cryo data acquisition. The photo of Marie Curie isfrom the nobelprize.org website.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jsb.2012.05.019.

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