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Akanksha Thapliyal

A sparse signal in a high dimensional space, compressive sensing system, which combines with sampling and compression, can reconstruct that signal accurately and efficiently from fewer linear measurements much less than its actual dimension using sparse priors of signal. Currently, researchers always use orthogonal wavelet to represent the images. But the wavelet only has single scaling function and can not simultaneously satisfy the orthogonality, high vanishing moments, compact support, symmetry characteristic and regularity. Developed from the theory of wavelet, multi-wavelet transform, which can simultaneously satisfy the five characteristics, provides a great potential to obtain high-performance coding. According to the three main steps (Sparse representation, measurement matrix, reconstruction algorithm) of compressive sensing image reconstruction, this paper proposes a compressive sensing image reconstruction based on sparse representation of the image in multi-wavelet transform domain while using Orthogonal Matching Pursuit iterative as the reconstruction algorithm. The experimental results show that the reconstructed image has batter vision quality and a good performance on PSNR. Meanwhile, the algorithm of reconstruction gets a faster convergence rate.