Accelerated MRI techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated MRI is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped formulate mathematical principles and conditions that ensure recovery of (structured) sparse signals from undersampled, incoherent measurements. In this paper, a new recovery algorithm, motion-adaptive spatio-temporal regularization (MASTeR), is presented. MASTeR, which uses compressed sensing principles to recover dynamic MR images from highly undersampled k-space data, takes advantage of spatial and temporal structured sparsity in MR images. In contrast to existing algorithms, MASTeR models temporal sparsity using motion-adaptive linear transformations between neighboring images. The e ciency of MASTeR is demonstrated with experiments on cardiac MRI for a range of reduction factors. Results are also compared with k-t FOCUSS with motion estimation and compensation|another recently proposed recovery algorithm for dynamic MRI.
This package provides various MATLAB codes for reconstructing quality cardiac MR images from highly under-sampled k-space data. The main theme in this work is to exploit spatial and temporal structure/sparsity of the MR images during their reconstruction.
Imaging model: Consider a dynamic MRI setup in which data consist of T images in a cardiac cycle. The vector form of the imaging system for an th image can be written as
is a complex-valued MR image, is a vector with k-space measurements of , is the encoding matrix which consists ofsubsampled Fourier transform weighted by coil sensitivity maps, and is the noise in the measurements.
Recovery problem: To recover image sequence from all the available k-space data , we solve a convex optimization program of the following general form:
The first term keeps the signal estimate close to the measurements and the second term promotes certain spatial/temporal sparse structure in . For instance, wavelet transform or total-variation operator for can be used for spatial sparse representation and linear or motion-adaptive temporal differences can be used for temporal sparse representation.
The code provides various options/combinations for sampling schemes, L1/L2 spatial/temporal regularizations (spatial: orthogonal or complex wavelet transform; temporal: frame difference, temporal DFT, motion-adaptive transforms), and more. Consult demo and job files for further details.
· M. Salman Asif, Lei Hamilton, Marijn Brummer, and Justin Romberg, Magnetic Resonance in Medicine, Accepted September 2012.
MASTeR models temporal sparsity using motion-adaptive linear transformations between neighboring images. Spatial transform using dual-tree complex wavelet transform (DT-CWT) and motion estimation using phase of DT-CWT coefficients.
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