Compressed Sensing Based on the Contourlet Transform for Image Processing
In the compressed sensing, the sparse image is the prior condition. Contourlet transform is a non-adaptive multi-directional and multi-scale geometric analysis method, which could represent the image with contour and texture-rich more effective and has st
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Compressed Sensing Based on the Contourlet Transform for Image Processing Qing Lei, Bao-ju Zhang, and Wei Wang
Abstract In the compressed sensing, the sparse image is the prior condition. Contourlet transform is a non-adaptive multi-directional and multi-scale geometric analysis method, which could represent the image with contour and texture-rich more effective and has strong capability of nonlinear approximation. In this chapter, based on the advantages of Contourlet transform and the theory compressed sensing, an improved compressed sensing algorithm based on Contourlet transform was proposed. The improved compressed sensing algorithm only measured the high-pass Contourlet coefficients of the image but preserving the low-pass Contourlet coefficients. Then the image could be reconstructed by the inverse Contourlet transform. Compared with the traditional wavelet transformation in the compressed sensing image application, simulation results demonstrated that the proposed algorithm improved the quality of the recovered image significantly. For the same measurement number, the PSNR of the proposed algorithm was improved about 1.27–2.84 dB. Keywords Contourlet transform • Compressed sensing • Image processing
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Introduction
The sparse image representation plays an important role in the compressed sensing (CS), image denoising, image inpainting and super resolution and so on [1]. The wavelet transform is the optimal approximation in the representation of point singularity of piecewise smooth function. However, for the two-dimensional image information, the wavelet transform is inadequate in the areas of image multi-directional expression. Therefore, in order to seek more effective methods
Q. Lei • B.-j. Zhang • W. Wang (*) Department Physics and Electronic Information, Tianjin Normal University, Tianjin, China e-mail: [email protected] Q. Liang et al. (eds.), Communications, Signal Processing, and Systems, Lecture Notes in Electrical Engineering 202, DOI 10.1007/978-1-4614-5803-6_18, # Springer Science+Business Media New York 2012
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than wavelet transform sparse representation, the Do and the Vetterli proposed the Contourlet Transform algorithm, which expressed the edge and the texture of the image sparsely [2]. Compared to previous wavelet transform, the Contourlet transform can overcome the limitations of the wavelet transform. Contourlet transform has the better direction selectivity, and it can meet the nature of the image sparely. Therefore, this chapter uses Contourlet transform algorithm as the image sparse representation method. This method has the better restore original image by solving the inverse problems in the areas of compressed sensing. In 2006, the Donoho and the Candes proposed a new sampling theory—the theory of compressed sensing [3, 4], which broke through the Nyquist sampling theorem. In recent years, compressed sensing has a great future. Such as: radar, imaging, image processing, data reconstruction and so on. And the image processing has the most rapid deve
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