基于SVD和能量最小原则的图像自适应降噪算法

基于奇异值分解和能量最小原则,提出了一种自适应图像降噪算法,并给出了基于有界变差的能量降噪模型的代数形式。通过在矩阵范数意义下求能量最小,自适应确定去噪图像重构的奇异值个数。该算法的特点是将能量最小法则和奇异值分解结合起来,在代数空间中建立了一种自适应的图像降噪算法。与基于压缩比和奇异值分解的降噪方法相比,由于该算法避免了图像压缩比函数及其拐点的计算,因此具有快速去噪和简单可行的优点。实验结果证明,该算法是有效的。

An Adaptive Image Denoising Algorithm Based on SVD and Energy Minimization

Based on SVD(Singular value decomposition) and the energy minimum principle,an adaptive image denoising algorithm is proposed in this paper.An energy model of image denoising in matrix norm is presented for restoring noisy image.By minimizing energe on the matrix norm,the singular number of the reconstructed image is adaptively determined.Comparing with the adaptive denoising algorithm based on compression ratio and SVD,it avoids calculating the function of image compression ratio and its knee point.Furthermore,it avoids solving nonlinear partial differential equation numerically comparing with the energy minimization denoising model of bounded variation,and so it never leads to local minimum in general.Our method can denoise rapidly and effectively.It can be also implemented easily in practice.Experimental results in the paper validate our proposed method.