Bandelets Based On Image Sparse Representation And Its Application

Sparse representation of image is a researching hotspot in image processing. The multiscale geometric analysis (MGA) can make full use of intrinsic geometric regularity of images. When it represents the lines or the singularity of curve, it uses fewer basis functions, which achieves more sparse representation. Bandelets is a new MGA tool which can implement an adaptive approximation of image geometry. As a piecewise C²(a> 2)regular function, it can represent the geometric regular images efficiently. We give more analysis of bandelets base on image sparse representation, and our main work can be summarized as follows:(1) The improvement of geometric flow of Bandelets. Based on the analysis of the relation between the geometric and the Lagrange function, a new method for determining the best geometry is proposed in this paper using similar binary search algorithm, which decrease the time complexity to O(log₂N²(log₂N)² )(for image of N×N pixels). And we use this algorithm to latter work.(2) The ROI image compression based on improved Bandelets. The proposed method codes the ROI and BG with different coding method. First, The ROI image is coded by Bandelets, and the ROI bitplane is shifted down, which is lower than BG bitplane. Then, the BG image is coded by SPIHT algorithm. Experimental results show that the proposed method has good performance than maxshift in both PSNR and vision, especially BG image.(3) Image Compression based on LP and Bandelets. Firstly, the image is decomposed by LP to get a coarse image and a detail image. Then we code the detail image with SPIHT algorithm, and the coarse image is decomposed by a Bandelets transform followed by entropy coding. Some experiments are taken on some images and the results show that our proposed scheme outperforms SPIHT and the second generation Bandelets methods in both PSNR and vision, especially texture image.(4) The CS reconstructed algorithm based on nested iterative optimization. This algorithm is based on the analysis of Iterative Hard Thresholding (IHT). It uses bandelets and wavelets as the sparse basis respectively, which can capture more image information. Several experiments show that the proposed reconstructed algorithm yields some improvements over other CS reconstructed algorithms in PSNR.