A novel singular value decomposition-based similarity measure method for non-local means denoising

Many methods have been proposed for image denoising, among which the non-local means (NLM) denoising is widely used for fully exploiting the self-similarity of natural images. For NLM denoising, it needs to calculate the similarity of clean image blocks as weights. But affected by noise, it is challenging to accurately get the similarity of clean image patches. Most existing NLM denoising approaches often cause the restored image to be over smoothed and lose lots of details, especially for image with high noise levels. To tackle this, a novel singular value decomposition-based similarity measure method is proposed, which can effectively reduce the disturbance of noise. For the method, we first calculate and vectorize the singular values of two image patches extracted from the noisy image and compute Euclidean distances and cross-angles of the vectors. Second, we propose to utilize the geometric average of Euclidean distance and cross-angle to calculate the similarity between two image patches which is resistant to noise. Third, the proposed similarity measure is applied to non-local means denoising to compute similarity of noisy image patches. Experimental results show that compared to state-of-the-art denoising algorithms, the proposed method can effectively eliminate noise and restore more details with higher peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) index values.