The application of compressed sensing (CS) to biomedical imaging is sensational since it permits a rationally accurate reconstruction of images by exploiting the image sparsity. The quality of CS reconstruction methods largely depends on the use of various sparsifying transforms, such as wavelets, curvelets or total variation (TV), to recover MR images. As per recently developed mathematical concepts of CS, the biomedical images with sparse representation can be recovered from randomly undersampled data, provided that an appropriate nonlinear recovery method is used. Due to high under-sampling, the reconstructed images have noise like artifacts because of aliasing. Reconstruction of images from CS involves two steps, one for dictionary learning and the other for sparse coding. In this novel framework, we choose Simultaneous code word optimization (SimCO) patch-based dictionary learning that updates the atoms simultaneously, whereas Focal underdetermined system solver (FOCUSS) is used for sparse representation because of a soft constraint on sparsity of an image. Combining SimCO and FOCUSS, we propose a new scheme called SiFo. Our proposed alternating reconstruction scheme learns the dictionary, uses it to eliminate aliasing and noise in one stage, and afterwards restores and fills in the k-space data in the second stage. Experiments were performed using different sampling schemes with noisy and noiseless cases of both phantom and real brain images. Based on various performance parameters, it has been shown that our designed technique outperforms the conventional techniques, like K-SVD with OMP, used in dictionary learning based MRI (DLMRI) reconstruction.
Transformed domain sparsity of Magnetic Resonance Imaging (MRI) has recently been used to reduce the acquisition time in conjunction with compressed sensing (CS) theory. Respiratory motion during MR scan results in strong blurring and ghosting artifacts in recovered MR images. To improve the quality of the recovered images, motion needs to be estimated and corrected. In this article, a two-step approach is proposed for the recovery of cardiac MR images in the presence of free breathing motion. In the first step, compressively sampled MR images are recovered by solving an optimization problem using gradient descent algorithm. TheL1-norm based regularizer, used in optimization problem, is approximated by a hyperbolic tangent function. In the second step, a block matching algorithm, known as Adaptive Rood Pattern Search (ARPS), is exploited to estimate and correct respiratory motion among the recovered images. The framework is tested for free breathing simulated andin vivo2D cardiac cine MRI data. Simulation results show improved structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and mean square error (MSE) with different acceleration factors for the proposed method. Experimental results also provide a comparison betweenk-tFOCUSS with MEMC and the proposed method.