【作者】 刘国庆；

【导师】 林京；

【作者基本信息】 合肥工业大学 ， 计算数学， 2011， 硕士

【摘要】 本文系统地介绍了压缩感知这一信号处理技术中新兴领域的有关基本概念，分析了现有的信号重构方法的优缺点。根据二维图像小波变换系数层的特点和现实应用中稀疏度未知的情况，提出了基于单层小波变换的自适应压缩感知新算法，保留图像低频系数，只针对高频系数进行测量。详细地说，在图像重构时，利用稀疏度自适应匹配追踪算法对高频系数或逐行或逐列或整体进行恢复，再进行小波逆变换重构图像。仿真结果表明，与单层小波变换的非自适应压缩感知算法相比，解决了稀疏度未知情况下的图像恢复问题，且重构图像质量也得到很好的保证。在相同的采样率下，PSNR相差不过2dB。更多还原

【Abstract】 In this thesis we systematically introduce the related basic concepts aboutcompressed sensing, a newly-developing field in signal processing techniques andanalyze the advantages and disadvantages of the current algorithms for the signalreconstruction. According to the properties of wavelet transform sub-bands and theunknown sparsity in many practical applications, an improved adaptive compressedsensing algorithm based on the single layer wavelet transform was proposed, whichonly measured the high-pass wavelet coefficients of the image but preserving thelow-pass wavelet coefficients. For the reconstruction, by using sparsityself-adaptive matching pursuit (SAMP) algorithm, high-pass wavelet coefficientscould be recovered by row, column or whole of the measurements. Then the imagecould be reconstructed by the inverse wavelet transform. Compressed with theoriginal compressed sensing algorithm based on the single layer wavelet transform,simulation results demonstrated that the proposed algorithm solve the problem ofimage reconstruction in the case of unknown sparsity, and the quality of therecovered image is guaranteed. For the same sampling rate, the PSNR difference ofthe proposed algorithm and the original algorithm is not greater than2dB.更多还原