Image Reconstruction Based On Compressed Sensing

The emerging Compressed Sensing (CS) theory suggests that it is likely to recoverthe signals from highly undersampled measurements, if the signal have a sparse repre-sentation under some transform domain and the sparse transform matrix and the sensingmatrix are incoherent. The researchers have introduced the CS theory to the MagneticResonance (MR) imaging, to speed up the imaging without degrading the image qual-ity. My research deals with how to efciently recover the target MR image from highlyundersampled k-space data. The major contribution of this thesis is summarized asfollow:(1) In order to improve the quality of the reconstructed MR image, which may beover-smoothed or may sufer from aliasing artifacts, the reconstruction problem is for-mulated as a constrained minimization problem with compound regularization terms,which is then solved by an efcient algorithm proposed. In the proposed algorithm, theoriginal constrained problem is reformulated as a sequence of unconstrained problemsby using the Bregman iteration. Then, by using the operator splitting technique, eachunconstrained problem can be decomposed into a gradient problem and a denoisingproblem which can be solved by the Split Bregman Denoising (SBD) algorithm. Then,the solving process of unconstrained problems is accelerated by using an acceleratedscheme. We call the proposed algorithm as BFSA (Bregman based Fast SBD Algo-rithm). For non-Cartesian grid sampling, an updating method is proposed for the stepsize L. Comparisons with the previous algorithms indicate that the proposed algorithmsignificantly improves the quality of the reconstructed images.(2) In order to speed up the reconstruction of the dynamic MR Imaging (dMRI), anefcient algorithm called ktBFSA is proposed based on the BFSA framework. ktBFSAuses the SBD3D (Split Bregman Denoising for3D images) to solve the3D image de-noising problem with compound regularization terms. Comparisons with the previousalgorithms indicate that the proposed algorithm not only significantly speeds up thereconstruction, but also improves the quality of the reconstructed images.(3) In order to speed up the Sensitivity encoding (SENSE) reconstruction for par- allel MR imaging, an efcient algorithm called FSRA (Fast SENSE ReconstructionAlgorithm) is proposed based on the BFSA framework. The experimental results showthat the proposed algorithm significantly reduces the reconstruction time. Autocalibrat-ing methods like SPIRiT (Iterative Self-consistent Parallel Imaging Reconstruction)implicitly use the sensitivity information for reconstruction and avoid some of the dif-ficulties associated with explicit estimation of the sensitivities. In order to improve thereconstruction quality, an efcient algorithm called ERAS (Efcient Reconstruction Al-gorithm for SPIRiT Based Parallel Imaging) is proposed. The proposed algorithm usesthe operator splitting technique to decompose the unconstrained problem into a gradientproblem and a denoising problem which can be solved by the joint-sparsity promotingalgorithm. And then the proposed algorithm is accelerated by using an acceleratedscheme. The experimental results show that the proposed algorithm significantly im-proves the reconstruction quality.(4) In addition, in order to seek for applications of compressed sensing in videocoding and improve the coding efciency of video coding, a compressed sensing basedimproved video coding scheme is proposed. This scheme choose the method produc-ing an image block with smaller sum of squared diference as the final reconstructionmethod between the standard method and the Total Variation (TV) minimization in thepixel domain, which is based on the fact that the original image has sparser gradientthan the residual image. The improved scheme is then integrated into the standardMPEG-2and H.264encoder. The experimental results show that the new encoder canimprove the coding efciency to some degree.