Research On OMP-based Compressed Sensing Algorithm

Compressed Sensing (CS) is a novel theory about signal acquisition. It breaks the restrictions of the Nyquist sampling theorem. The Nyquist sampling frequency is determined by the frequency of signal, while the signal sampling frequency of CS is depended on the structure and content of signal. The sample values are collected and compressed appropriately in the process of signal acquisition.The codec frame of CS is not symmetrical. The sample values are projected by the measurement matrix in compression process, so its operation is relatively simple. However, the process of the decoding is much complex, as it involves the complicated reconstruction operation. The un-symmetric framework is able to meet the actual demand.A novel CS algorithm based on orthogonal matching pursuit is researched seriously. In order to speed up reconstruction process, two parallel schemes of CS are proposed. Then a CS algorithm for color image is researched. The major works in the paper are as follows.A CS parallel processing algorithm proposed is implemented by OpenMP, and two parallel structures of the sparse transform-DCT and DWT-are analyzed. An image is blocked, so that the process of DCT can be executed independently. Then transformed coefficients are rearranged and performed by the order of frequency. The correlations of DWT coefficients decrease, and filter process between rows and columns can be executed independently. Transformed coefficients are divided into different sub-blocks which can be compressed separately by the measurement matrix. In the end, each sub-block can be separately reconstructed. This method not only reduces the amount of data computing, but also the number of iterations in the orthogonal matching pursuit algorithm. With OpenMP, the time of sparse transform, measurement and reconstruction processes in CS is effectively reduced.The selected CS parallel processing algorithm with OpenMP is proposed. In order to improve the quality of reconstructed image, only the higher frequency coefficients after sparse transform are compressed by CS. This algorithm improved the quality of reconstructed image when rate is lower.The multiple description of CS parallel processing algorithm with OpenMP draws on the thought of multiple description coding. The sparse transformed coefficients are divided into several descriptions using interleaving extraction, each description is distributed into multiple threads and executed the measurement and reconstruction concurrently. The proposed algorithm not only improves the efficiency of CS implementation, but also the quality of reconstructed image.A novel CS algorithm for color image is proposed, which further uses the correlation of color channel to implement compressed sensing. The color image is transformed by RGB-YUV firstly, and the sparse coefficient in different channel is compressed under different compression ratio. The quality of reconstructed image by proposed algorithm is improved, so does the subjective visual effect.