Compressed Sensing Reconstruction Using Structural Dependency Models

Abstract

Compressed sensing (CS) theory has demonstrated that sparse signals can be reconstructed from far fewer measurements than suggested by the Nyquist sampling theory. CS has received great attention recently as an alternative to the current paradigm of sampling followed by compression. Initial CS operated under the implicit assumption that the sparsity domain coefficients are independently distributed. Recent results, however, show that exploiting statistical dependencies in sparse signals improves the recovery performance of CS. This dissertation proposes model-based CS reconstruction techniques. Statistical dependency models for several CS problems are proposed and incorporated into different CS algorithms. These models allow incorporation of a priori information into the CS reconstruction problems. Firstly, we propose the use of a Bayes least squares-Gaussian scale mixtures (BLS-GSM) model for CS recovery of natural images. The BLS-GSM model is able to exploit dependencies inherent in wavelet coefficients. This model is incorporated into several recent CS algorithms. The resulting methods significantly reduce reconstruction errors and/or the number of measurements required to obtain a desired reconstruction quality, when compared to state-of-the-art model-based CS methods in the literature. The model-based CS reconstruction techniques are then extended to video. In addition to spatial dependencies, video sequences exhibit significant temporal dependencies as well. In this dissertation, a model for jointly exploiting spatial and temporal dependencies in video CS is also proposed. The proposed method enforces structural self-similarity of image blocks within each frame as well as across neighboring frames. By sparsely representing collections of similar blocks, dominant image structures are retained while noise and incoherent undersampling artifacts are eliminated. A new video CS algorithm which incorporates this model is then proposed. The proposed algorithm iterates between enforcement of the self-similarity model and consistency with measurements. By enforcing measurement consistency in residual domain, sparsity is increased and CS reconstruction performance is enhanced. The proposed approach exhibits superior subjective image quality and significantly improves peak-signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).Finally, a model-based CS framework is proposed for super resolution (SR) reconstruction. The SR reconstruction is formulated as a CS problem and a self-similarity model is incorporated into the reconstruction. The proposed model enforces similarity of collections of blocks through shrinkage of their transform-domain coefficients. A sharpening operation is performed in transform domain to emphasize edge recovery. The proposed method is compared with state-of-the-art SR techniques and provides high-quality SR images, both quantitatively and subjectively.