image reconstruction and image priors
DESCRIPTION
Image reconstruction and Image Priors. Tim Rudge Simon Arridge, Vadim Soloviev Josias Elisee, Christos Panagiotou Petri Hiltunen (Helsinki University of Technology). Fast reconstruction algorithm Edge-based image priors Joint entropy image priors Gaussian-mixture classification priors. - PowerPoint PPT PresentationTRANSCRIPT
Image reconstruction and Image Priors
Tim Rudge
Simon Arridge, Vadim Soloviev
Josias Elisee, Christos Panagiotou
Petri Hiltunen (Helsinki University of Technology)
1. Fast reconstruction algorithm
2. Edge-based image priors
3. Joint entropy image priors
4. Gaussian-mixture classification priors
1. Fast reconstruction
Image compression method Reduce matrix size Explicit fast inversion Optics Letters, Vol. 35, Issue 5, pp. 763-765
(2010)
Measurement setup
Forward operator
•Size of matrix A = (nx* n
y* n
s* n
θ) x n
recon = very big
i,j = source, detectorw = pixel detector profileP = projection to imageS = diag(1/ye) = normalisationGf / Gf* = Green's operator / adjoint operator (fluorescent λ)Ue = excitation field
Compress each image
Where rows of Z:
...are basis functions in image
E.g. Wavelets, Fourier (sine/cosine)
Form compressed system
By replacing window functions w, with basis functions z in:
Size of matrix = (nz* n
s* n
θ) x n
recon = more reasonable
Solve compressed system
Matrix is (nz* n
s * n
θ) x (n
z* n
s * n
θ)
Small enough to store and solve explicitlyTypically solves in < 10s
Some results
Redundancy in data
2. Edge priors
•Smoothing operator
•Spatially varying width
•Edge in prior image low smoothing
•Smoothing max. ║ to edge
•Prior image flat max. Smoothing
•No segmentation needed
Huber edge prior (region), simulated data 2% noise
3. Joint entropy priors
4. Gaussian-mixture priors
•Tikhonov 0 == single Gaussian
•Use mixture of k Gaussians
•Iteratively:
•K-means cluster class statistics
•Construct inv. covariance Cx-1, mean μx
•Reconstruct with prior Cx-1, μx
x
x,Cx
y Cy
Data Noise Statistics
Image
Image Statistics Class Statistics
ReconstructionStep
EstimationStep
Prior UpdateStep
Combined Reconstruction Classification
Anim2d.mov
People / papers
Petri Hiltunen (Helsinki) – Gaussian-mixture priors Phys. Med. Biol. 54, pp. 6457–6476, (2009)
Christos Panagiotou – Joint entropy priors J. Opt. Soc. Am., Vol. 26, Issue 5, pp. 1277-1290, (2009)
Wavelet method: Optics Letters, Vol. 35, Issue 5, (2010) pp. 763-765, (2010)
Martin Schweiger TOAST FEM code, other programming
Josias Elisee BEM method
Vadim Soloviev, Thanasis Zaccharopolous, Simon Arridge