Learning-based Compressive Sensing Image Recovery

The digital signal acquisition from continue signal plays an important role in digital signal processing system. Conventional signal acquisition systems sample a signal at a rate of at least two times its bandwidth for the perfect signal reconstruction, and then compress the sampled data for storage and transmission. The compressive sensing theory gives rise to a new solution to signal acquisition and reconstruction. It supports sensing directly the compressed data by random projection at extremely low rate, and thus significantly saves the system resource. The perfect signal reconstruction from the linear measurements is guaranteed with extremely high probability by the compressive sensing theory. However, how to accurately recover the original signal from the measurements is an important open problem. The key issue of the compressive signal recovery lies in the selection of the sparse domain, where the original signal exhibits the highest sparsity is the key problem. In this thesis, we proposed a learning-based approach to solve the sparse domain selection problem, and thus significantly improve the quality of compressive signal recovery. To further improve the learning-based approach, we also studied the nonlocal self-similarity based compressive signal recovery.In this thesis, we first introduce the learning-based compressive image recovery algorithm. The conventional compressive recovery algorithms use the fixed sparse domains (e.g. DCT, wavelet and gradient), which are unable to accurately characterize the local image structures, and thus fail to recover the fine image details. To solve this problem, we proposed to learn a set of piecewise autoregressive image models from a set of example image patches. The learned image models are adaptively selected to construct the locally adaptive sparse domains for sparse representation of the image structures. Experimental results show that the proposed learning-based recovery algorithm can significantly outperform conventional recovery algorithms. In addition, since the model learning is performed in an offline process, the computational complexity of the proposed approach is comparable to the conventional approach.To further improve the image recovery quality, this thesis also proposed a nonlocal self-similarity based compressive recovery algorithm. Through adaptive model selection, we can characterize the local sparse domain overcoming the drawback of the conventional recovery methods. However, the pixel-wise model adaptation may cause the inconsistence between neighboring pixels, and thus generate artifacts. On the other hand, natural images often contain self-repetitive structures, which can be used to construct a nonlocal self-similarity constraint. By introducing the additional regularization term, we can significantly improve the quality of the sparse signal reconstruction.As an application of the compressive sensing, this thesis studied the compressive sensing based multiple image coding (CS-MDC). Conventional MDC can only generate limited number of descriptions and suffer from the packet loss. The CS-MDC has the advantages of generate arbitrary number of descriptions and high anti-packet loss. To improve the rate distortion performance of the CS-MDC, we applied the proposed compressive image recovery algorithm for MDC. Experimental results show that the proposed model-based recovery method can significantly improve the rate-distortion performance of the CS-MDC.