compressive sensing in dt-mri
DESCRIPTION
Results for DT MRI. COMPRESSIVE SENSING IN DT-MRI. Daniele Perrone 1 , Jan Aelterman 1 , Aleksandra Pižurica 1 , Alexander Leemans 2 and Wilfried Philips 1. 1 Ghent University - TELIN - IPI – IBBT - St.-Pietersnieuwstraat 41, B-9000 Gent, Belgium. - PowerPoint PPT PresentationTRANSCRIPT
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COMPRESSIVE SENSING IN DT-MRICOMPRESSIVE SENSING IN DT-MRIDaniele Perrone1, Jan Aelterman1, Aleksandra Pižurica1,
Alexander Leemans2 and Wilfried Philips1
1 Ghent University - TELIN - IPI – IBBT - St.-Pietersnieuwstraat 41, B-9000 Gent, Belgium
Diffusion Tensor Magnetic Resonance Imaging (DT- MRI) can infer the orientation of fibre bundles within brain white matter tissue using so-called Fiber Tractography (FT) algorithms. The data capture step force to choose a trade off between data quality and acquisition time.
What is Diffusion Tensor MRI?
MRI scanner
The color image
It is not possible to acquire fewer data without losing information and eventually generating corruption in images...
…is it possible to discard only “superfluous” information?
Focusing on the problem
No artifacts
Shearlets can represent natural image optimallywith only a few significant (non-zero) coefficients, while noise and corruptions would need more coefficients.
We can force a noise and artifact free reconstruction.
Why shearlet transform?
Results for DT MRI
Split Bregman technique
Considering just the Fourier samples that are not attenuated:
• the number of samples is less than the number of image pixels an infinite number of possible image reconstructions;
• naively filling in the missing data in Fourier space leads to artifacts in MRI and therefore in FT reconstruction;
• proposed: Compressive Sensing (CS) reconstruction we have an infinite number of possible image reconstructions we do want to maintain fidelity to the acquired data
we can choose the image that is representable with the LOWEST number of coefficients possible in the shearlet domain ( that corresponds to the minimum number of image structures )
Speeding up with Compressive Sensing
2 Image Sciences Institute - University Medical Center - Heidelberglaan 100, 3584 Utrecht, the Netherlands.
Full brain acquisition( axial view )
Formalization of the problem :
* N ( N different directions )
Gibbs ringing artifact in IMAGE DOMAIN
Wrong - even negative ! - eigenvalues inDIFFUSION TENSOR DOMAIN
FiberTract.
IFFT
IFFT
IFFT
FiberTract.
FiberTract.
FiberTract.
- number of fiber tracts- mean length of the fiber tracts- fractional anisotropy- apparent diffusion coefficient- mean value and variance of the three eigenvalues
Compr. SensingK-space
reconstruction
Promising quantitative improvements considering :
FFT
50%FFT
Fiber Tractography SEED(corpus callosum - sagittal view)
Brain tracts( coronal view )
Brain tractography( coronal view )
Split Bregman algorithm :
Image domain: experiment50% of the coefficients usedPSNR of the reconst. image: 40 dBGibbs artifact : ABSENTTheoretical acquisition speedup: 2
f is C² (edges:piecewise C²)
Approximation error:
Fourier basis : ε M ≤ C * M -1/2
Wavelet basis : ε M ≤ C * M -1
Shearlet tight frame : ε M ≤ C * (log(M))3 * M-2
x* = argmin |Sx| so that ||y – Fx||2
x
xi+1 = argmin λ/2||Fx - yi||2 + μ/2||di - Sx - μi||2
di+1 = argmin |d| + μ/2||d - Sxi+1 - μi||2
μ = μi + Sxi+1 - di+1
goto 1 until convergence of μi+1
yi+1 = yi + y - Fxi+1
goto 1 until convergence of yi+1
x
d
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CS