MR Image reconstruction based on compressed sensing

The sparsity which is implicit in MR images is exploited to significantly undersample k-space. According to the developed mathematical theory of Compressed-Sensing (CS), images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used to reducing the MRI scan duration. In order to overcome the poor directional selectivity of orthogonal wavelet bases which is used as a sparsifying transform, Our algorithm is based upon the contourlet transform, And then a reconstruction algorithm is proposed, which combines contourlet with the iterative thresholding algorithm. The calculations are accelerated by continuation and takes advantage of contourlet and Fourier transforms enabling our code to process MR images from real-life applications. In this paper, the reconstruction is performed by minimizing the ℓ 1 norm of a transformed image, subject to data fidelity constraints. Experiment results show that the proposed algorithm improves the visual quality, protects image details, and accelerates the convergence of reconstruction algorithm.