Image Denoising Using Block Matching Tensor Approximation (BMTA)
Associated People:
Elena Braverman (University of Calgary)
Bin Han (University of Alberta)
Yi Shen (University of Calgary and University of Alberta)
Associated Sites:
PIMS University of Alberta
Associated Sites:
PIMS University of Calgary
Associated PIMS Programs:
Applied and Computational Harmonic Analysis: 2011-2014
Figure 1: (a) Original color image of kodim03, (b) Noisy image with σ = 40, (c) Denoised image by CBM3D, (d) Denoised image by our proposed BMTA.
Digital datasets collected by imaging sensors are often corrupted by additive white Gaussian noise. Image denoising for grayscale images and color images is one of the fundamental problems in the field of image processing. Using block matching and tensor approximation, we study image denoising to restore grayscale images or color images contaminated by additive white Gaussian noise. The basic idea of our method is as follows: group similar patches as third order tensors, perform higher order singular value decomposition for each tensor, and then apply softhresholding for tensor approximation. Therefore, we call our algorithm as the block matching tensor approximation (BMTA) for grayscale image denoising. Experimental results show that the overall performance of our proposed algorithms is comparable or better than several known state-of-the-art image denoising methods.
Let F be a clean color image and F-hat be a denoised color image, for color images, peak signal to noise ratio (PSNR) is defined to be
PSNR is used to measure the denoising quality. The higher the value of PSNR, the lower the error. To compare with the state-of-the-art image denoising methods CBM3D [1], 24 color images from the Kodak gallery [2] are used. The results are reported in Table 1
| Image No. | BMTA | CBM3D | Image No. | BMTA | CBM3D |
| 1 | 27.02 | 26.48 | 13 | 24.96 | 24.57 |
| 2 | 29.96 | 29.46 | 14 | 27.57 | 27.13 |
| 3 | 31.55 | 30.89 | 15 | 28.99 | 28.50 |
| 4 | 30.41 | 29.82 | 16 | 30.18 | 29.60 |
| 5 | 26.76 | 26.26 | 17 | 29.34 | 28.97 |
| 6 | 27.66 | 27.17 | 18 | 26.99 | 26.64 |
| 7 | 30.58 | 30.23 | 19 | 29.62 | 29.14 |
| 8 | 26.87 | 26.34 | 20 | 26.37 | 25.87 |
| 9 | 31.73 | 31.19 | 21 | 28.53 | 28.09 |
| 10 | 31.21 | 30.66 | 22 | 28.79 | 28.39 |
| 11 | 28.51 | 28.09 | 23 | 31.76 | 31.24 |
| 12 | 31.04 | 30.58 | 24 | 27.24 | 26.64 |
Table 1: The 24 test color images are from the Kodak gallery. Comparison results on color image denoising with standard deviation of noise being 40. The range of the noisy image is scaled to be within [0, 255] before testing.