Objective

2

Images are often distorted by noise during image acquisition

transmission and storage process. The generated noise can degrade image quality and affect image processing

such as edge detection

image segmentation

image recognition and image classification. Image denoising technique plays a key role in image pre-processing for image details preservation. Current Gaussian noise removal denoising techniques is often based on variational model like the total variation (TV) method. It can realize image smoothing through minimizing the corresponding energy function. However

TV-based denoising methods have their staircase effects and detail loss due to local gradient information only. Many researchers integrate the non-local concept into the total variation model after the non-local means was proposed. The existing non-local TV-based methods take advantages of the non-local similarity to denoise the image while keeping the image structure information. Unfortunately

many existing TV-based color image denoising methods fail to fully capture both local and non-local correlations among different image patches

and ignore the fact that the realistic noise varies in different image patches and different color channels. These always lead to over-smoothing and under-smoothing in the denoising result. Our newly TV-based color image denoising method

named adaptive non-local 3D total variation (ANL3DTV)

is developed to deal with that.

Method

2

1) Decompose the noisy color image into

K

overlapping color image patches

search for the

m

most similar neighboring image patches to each center image patch and then group the

m

image patches together. 2) Vectorize every color image patch in each image patch group and stack them into a 2D noisy matrix. 3) Obtain the corresponding 2D denoised matrices via ANL3DTV. To get the inter-patch and intra-patch correlations

our ANL3DTV takes advantages of a non-local 3D total variation regularization. On the basis of embedding an adaptive weight matrix into the fidelity term of the optimization model

it can automatically control the denoising strength on different color image patches and different color channels in each iteration. The weight matrix is correlated with the estimated noise level of each image patch. 4) Aggregate all the denoised 2D matrices to reconstruct the denoised color image.

Result

2

According to different ways to add Gaussian noise

there are two cases in the denoising experiment. In Case 1

the noisy images are corrupted with Gaussian noise with the same noise variance in all color channels. The selected noise levels are

σ

= 10

30 and 50. In Case 2

we add Gaussian noise with different noise variances to each color channel. The noise levels are [

σ

R

σ

G

σ

B

] = [5

15

10]

[40

50

30]

[5

40

15]

and [40

5

25]. ANL3DTV is compared to 6 existing TV-based denoising methods. The peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) are adopted to denoising evaluation. The averaged PSNR/SSIM results of ANL3DTV in Case 1 are 32.33 dB/92.99%

26.92 dB/81.68 and 24.57 dB/73.57%

respectively

and the quantitative results of ANL3DTV in Case 2 are 31.62 dB/92.88%

24.49 dB/73.02%

27.47 dB/85.94% and 26.81 dB/81.00%

respectively. Compared with other competing methods

ANL3DTV improves PSNR and SSIM by about 0.16~1.76 dB and 0.12%~6.13%. As can be seen from the denoised images

some competing methods oversmooth the images and lose many structure information. Some mistake noise pattern for the useful edge information and yield obvious ringring artifacts. Our ANL3DTV can remove more noise

preserve more details and suppress more artifacts than the competing methods.

Conclusion

2

We demonstrate an adaptive non-local 3D total variation model for Gaussian noise removal (ANL3DTV). To capture the inter-patch and intra-patch gradient information

ANL3DTV is focused on the non-local 3D total variation regularization. To adaptively adjust the denoising strength on each image patch and each color channel

an adaptive weight matrix into the fidelity term is introduced. To guarantee the feasibility of ANL3DTV mathematically

we develop the iterative solution of ANL3DTV and validate its convergence. The visual results demonstrate our ANL3DTV potentials in noise removal and detail preserving. Furthermore

ANL3DTV achieves more robustness and stablizes noise removal more under different noise levels.