Research And Applications Of Image Sparse Algorithm In Compressed Sensing

As a new sparse signal sampling theory, the compressed sensing (CS) breaked though the restrictions about the sampling rate of the Nyquist sampling theorem. Compressed sensing theory says:If the signal could be sparsed in a particular transform domain, we can use a random measurement matrix which is not related to the transform base to obtain a small amount of observational data. These observational data, combined with proper reconstruction algorithms can achieve a high probability of low-distortion signal or distortion-free reconstruction. Compared with the traditional signal compression, the compressed sensing technology compresses the signal, while sampling the data. It has effectively solved the contradiction between the sampling and compression in traditional signal processing.First, based on the research results of our group, a compressed sensing algorithm based on improved layered discrete cosine transform (DCT) was proposed, which only measured the high-pass coefficients of the other layers but preserving the top layer coefficients. For the reconstruction, high-pass coefficients could be recovered by the measurements. Then the image could be reconstructed by the inverse DCT transform. Simulation results demonstrated that the proposed algorithm improved the quality of the recovered image significantly.The study found that, although compressed sensing algorithm based on improved layered DCT which was applied to image compression and recovery can achieve good results, yet the improved layered DCT could not describe the image edge and contour information in the sparsest way. Contourlet transform is an image multiscale geometric analysis tool, and it can effectively represent the contour and texture image and has good nonlinear approximation ability. This paper proposes a compressed sensing algorithm based on Contourlet transform in the field of image processing. The algorithm uses Contourlet transform to sparses the image signal, and then observe the sparse signal with a random matrix. Finally, the paper used orthogonal matching pursuit algorithm to reconstruct the image. The experimental results show that the visual effect of reconstructed image is good.Finally, this paper compared compression and recovery results of the two sparse algorithms, while they were used to process the same image. The results show that, compared with the compressed sensing image sparse algorithm, the compressed sensing image sparse algorithm based on Contourlet transform can sparse image signal and maintain the details of the image better. For the same compression ratio, the peak signal to noise ratio of the former algorithm is improved about4-8dB.