Fractal Dimension based SAR Image Sparse Degrees Estimation

Compressed sensing is surprisingly predicts that images, which allow a sparse representation by a suitable basis or a frame, can be recovered from what was previously considered highly incomplete linear measurements by using efficient algorithms. It is a novel research area of SAR images processing. As a result of the design of the observation matrix estimate depends on the image sparse degree, therefore, the estimation precision of the image sparse degree is an important factor to whether can accurate reconstruction images. In this paper, the relationship between the degrees of SAR image sparse and fractal dimension is researched. The experimental results show that the SAR image fractal dimension is proportional to the sizes of the observation matrix, which can be used to set the parameters of the observation matrix. Introduction SAR image processing is a novel research area due to the nature of their day and all-weather. Compressed sensing theory used to study the SAR image data acquisition and compression, have very important significance. Compressed sensing theory is proposed based on image sparse, under the condition of sparse image satisfaction, and can be far less than the Nyquist frequency of image sampling, can recover higher accuracy of reconstructed data with appropriate reconstruction algorithms. If an image f with a length N is sparse under the orthogonal basis, it can be expressed in the formula , with a sparse matrix a. Observation image y is obtained by observation matrix , and , y have the length M and M<<N. Y is used to recover the image f by using the compressed sensing theory, its essence is to solve an abnormal condition equation, which equation size M is less than variable size N. This equation is supposed to have infinite solutions but it just have a one solution under the condition named limited isometric conditions [1] [2], In this case, the sparse degree k meet the formula (1). (1) Usually, for M=4k. For the accuracy of image reconstruction is depends on the sparse degree k, its estimation has important significance. At present, the image sparse research mainly in the image form and image model two aspects, the sparse model including Markov models, frequency models and dictionary models and so on. The analysis of image form was including the following works: literature [3] estimated the k by using the image complexity and edge characters; literature [2] used wavelet to express the k, literature [5] proposed a PCA based estimate method and etc. Meanwhile, the analysis of image model research works was focus on establish the image model of sparse express, the model parameters show the sparsity of images. Images were mapping to a new coordinate system, where they have k sparse parameters. These methods are realizable. For example, an image having time-varying information just has a few frequency components. This fact is this image is sparse in frequency domain. Wavelet is also an effective method to reduce the image components. All these methods are depends on the mapping space, and almost these methods have more complexity. This paper proposed a novel method to estimate the k by using computing the image fractal dimension. This paper reveals the relationship between fractal and sparse degree k, and obtained the mathematics description. This method is independent on the function basis and has a low complexity. 4th International Conference on Electrical & Electronics Engineering and Computer Science (ICEEECS 2016) Copyright © 2016, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Computer Science Research, volume 50