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小波阈值去噪是信号与图像去噪中的有效方法,然而,该方法采用逐点处理的方式,未用到小波系数的整体结构特性。文中提出一种新的小波去噪方法,采用了新近发展起来的稀疏表示工具,通过在一定条件下最小化非零小波系数的个数对原小波系数进行估计,从而将去噪转化为一个最优化问题.证明了该优化问题的解可以惟一获得,并且该解是干净小波系数的一个无偏估计值。文中提出了一种求解该问题的方法,该方法至少能求得一个局部最优解.实验结果表明此方法对多数实际信号尤其是低信噪比信号是有效的。
Wavelet threshold denoising is an effective method for signal and image denoising. However, this method adopts the method of point-by-point processing and does not use the overall structural characteristics of wavelet coefficients. In this paper, a new wavelet denoising method is proposed, which uses the newly developed sparse representation tool to estimate the original wavelet coefficients by minimizing the number of non-zero wavelet coefficients under certain conditions, so as to convert the denoising into a maximum It is proved that the solution of this optimization problem can be uniquely obtained, and the solution is an unbiased estimate of the clean wavelet coefficients. In this paper, a method to solve this problem is proposed, which can obtain at least a local optimal solution.The experimental results show that this method is effective for most real signals, especially low SNR signals.