BM3D-GT&AD: an improved BM3D denoising algorithm based on Gaussian threshold and angular distance

Block-matching and three-dimensional filtering (BM3D) is generally considered as a milestone for its outstanding performance in the area of image denoising. However, it still suffers from the loss of image detail due to the utilisation of hard thresholding on transform domain during the phase of the basic estimate. In the frequency domain, a large amount of image detail information is in high frequency, which tends to be mixed with noise. Since its low amplitude is below the threshold, some image detail is filtered out with the noise. To retain more details, this study proposes an improved BM3D. It adopts an adaptable threshold with the core of Gaussian function during hard thresholding, which can filter out more noise while retaining more high-frequency information. When grouping, the normalised angular distance is taken as a measure of similarity to relieve the interference of noise further and achieve a higher peak signal-to-noise ratio (PSNR). The experimental results show that under the background of Gaussian noise with standard deviation of 20-60, the PSNR of denoised images (with a large amount of detail), applied with the authors' improved algorithm, can be improved by $0.1 - 0.4 \, {\rm dB}$0.1-0.4dB compared with original BM3D.