Study Of Analytic And Trained Dictionaries For Sparse Representation And Its Applications To Medical Imaging And Image Processing

Inverse problems are ubiquitous in the field of medical imaging and image processing.Prominent examples include compressed image reconstruction and image denoising. The goalof these problems is to reconstruct or restore an unknown image from a set of direct/indirectmeasurements. However, due to the limitation of the acquisition time or the existence of noise,the obtained measurements are often corrupted or incomplete, which introduces bigchallenges for the reconstruction process. In order to remove the noise or overcome theill-posed nature caused by the insufficient measurements, it is necessary to explore the priorknowledge and utilize this to form the constraints in the reconstruction process so as to makeup for the missing or corrupted information. However, traditional prior knowledgeregularizations and their corresponding algorithms suffer from loss of the detailed informationsuch as texture and structure while reducing the image degradation factors. To this end, basedon the physiological findings about human visual system (HVS), this thesis focuses onexploiting the prior knowledge of patch-based similarity and sparsity and has developed aseries of novel algorithms with applications to diverse inverse problems. The main work andcontribution are summarized as follows:On one hand, from the angle of sparse representation over analytic dictionaries, the totalvariation (TV) based bias correction algorithm and Gabor feature based nonlocal means(GFNLM) algorithm have been proposed. Another algorithm on joint entropy regularized biasremoval has been proposed for magnetic resonance (MR) image restoration via exploring the isotropic and anisotropic total variation of the image. The bias field is modelled as the linearsum of k equidistant low frequency B-spline functions. The MR image is finally updated byremoving the estimated multiplicative bias field. GFNLM has been developed based on theseminal biological finding that two-dimensional Gabor functions can effectively describe theprofile of simple-cell receptive fields in the mammalian cortex. This filter utilizes the Gaborfilter banks to extract the texture features and then use them to calculate the similarity weightsbetween the targeted pixel and the pixels in the search window. The image restoration is atlast realized as replacing each pixel value with the weighted sum of these pixel values. Theexperimental results suggest that this algorithm can better balance the texture informationpreservation and white Gaussian noise removal.On the other hand, this thesis has proposed three dictionary learning based algorithms, namelythe dictionary learning based impulse noise removal (DL-INR) algorithm,the spatiallyadaptive constrained dictionary learning (SAC-DL) algorithm andthe Fenchel duality baseddictionary learning (FD-DL) algorithm. DL-INR uses the dictionary learning technique tocapture the structure information inherited in the image and the robustness of the data-fidelity term. In the implementation of the algorithm, the ima1-norm toregularize ge is firstseparated into a number of partially overlapping image patches; then a dictionary is learnedunder the1-1minimization; at last each image patch is recovered via the sparseapproximation of these dictionary atoms. This algorithm has been applied to a series ofimpulse noise corrupted images with promising restoration results achieved. SAC-DL istargeted to remove the signal-dependent Rician noise. It exploits the statistics of the imageFpaetncchheesl’asn ddu easlittiym athteeso rtehme ltooc aclo vnavreiratn tchee oofr iegaicnha li mpraigmea pl a tc2h-.F1D-DL uses a generalization ofminimization problem into adual formulation. The dual objective is then solved under the augmented Lagrangianframework. The Fenchel duality provides a theoretical basis for reducing the complexity ofspace to ation results.. In its application, the algorithm has presented encouragingrestor...