Synopsis

Keywords: Data Processing, Data Processing

In noise reduction, the lower the amount of noise, the lower the image degradation associated with the noise reduction. Using this property, we propose a new denoising scheme that can improve denoising performance using trained CNN. Noise suppressed image by low-pass filter is inputted to denoising CNN and then output image is enhanced by high-pass filter. Experimental results show that noise suppression of the input image improves both image structure preservation and noise processing performance. The proposed method was applied to a parallel blind image denoising method. As a results, further improvement in performance was shown.

Introduction

Denoising methods based on the convolutional neural network (CNN) are known for their excellent performance [1], however, it tends to blur the output image. In general, the less noise an image contains, the less image degradation due to noise reduction. Using this property, we propose a new denoising scheme that can improve denoising performance without any changes or an additional training of CNN. A low-pass filter is applied to suppressed noise on the image in the frequency space of the image (k-space), then the noise suppressed image is input to the denoising CNN. After noise reduction, the image is restored using a high-pass filter. Since the amplification of noise due to the high-pass filter is slight, the overall evaluation of proposed method can improve the structural preservation of the denoised image. To further improve the performance, the method was applied to Parallelized Blind Image Denoising method (ParBID), which can improve structure preservation and noise reduction performances [2-4].

Methods

We used Blind Denoising CNN (hereafter BDnCNN) as a denoising method, which is an adaptive noise reduction method for images with unknown noise levels [1,3]. Figure 1 shows the algorithm of proposed method. First, a low-pass filter G is multiplied in the Fourier transform space of the noisy image (k-space) to suppress noises. This noise suppressed image is then input to BDnCNN to obtain a denoised image. Since the sharpness of the CNN output image is reduced by the filter G, the higher frequency of output image is restored by an inverse filter of G. Hereafter, we call proposed method as NC-BDnCNN (Noise-Controlled Blind DnCNN). Low-pass filter G used in the experiments is written as,
$$$G(k_x,k_y)=\frac{1}{1+c ((k_x-N/2)^2+(k_y-N/2)^2)} ,$$$
where $$$(k_x,k_y)$$$ means the index of k-space ( $$$ k_x,k_y\leq N$$$). To further improve the structural preservation of images, NC-BDnCNN was applied to ParBID [4]. ParBID does not denoise the noise image $$$r_i$$$ itself, but rather the weighted summed images. For example, in the case of three slice images, image $$$I_i=a_{i-1} r_{i-1} +a_i r_i+a_{i+1} r_{i+1} $$$ is denoised. Noise reduction was performed on multiple weighted averaged images obtained by changing the weight $$$a_i$$$. The target slices are then separated by solving the inverse matrix using denoised image $$$I_i$$$.
Low-pass filter G was applied to weighted images $$$I_i$$$ and then denoising was performed to filtered images. Separated images slice by slices were restored by inverse filter of G.

Results & Discussions

In the training of the Blind DnCNN network, 900 MR images (T1W, T2W, PDW) were used for training and 50 images were used for denoising tests. Images with several noise levels were broken down into small patches, and these patches were then batched in such a way that patches with different noise levels were combined in a single batch. Figure 2 (a)-(c) show the PSNR and SSIM of denoised images at 2.5%, 5.0% and 7.5% noise level with reference to the parameter c, respectively. The value at c=0 means the PSNR and SSIM of BDnCNN. It was shown that the improvement in PSNR and SSIM was greatest when the noise level was 2.5% and the optimal value of $$$c$$$ depended on the noise level. Denoised image of 5.0% noise from c=0 to 1.0 are shown in Fig. 2 (d). Detailed structure of the image is sharpened in proportion to the parameter $$$c$$$ without significant amplification of noises. Denoised images at each noise levels are shown in Fig.3. BDnCNN images have a large degree of smoothing effect, while NC-DnCNN images have good preservation of detail structure, and are close to the reference image. In the case of 7.5% noise, even though the improvement in PSNR is small, the structure of the image is well preserved, as shown in Fig. 3 (t),(x). Proposed noise control scheme was applied to the traditional weighted nuclear norm minimization (WNNM) denoising method [5]. It was shown that there was an improvement of PSNR in BDnCNN, but no improvement in WNNM. These results indicate that noise control scheme is highly effective in denoising CNN.
The filter G is a simple filter but it strongly suppresses most of the noise in the high frequency range of the 2-D k-space, making it highly effective for noise reduction. In addition, the image information is preserved because no thresholding is executed in the space represented by some basis.
The results of application of ParBID are shown in Fig.4. The weight coefficients used for two or three slices were {{0.7,0.3},{-0.3,1.3}} and {{0.3, -0.8,1.0},{0.2,0.6,0.2},{1.0,-0.8,0.3}}[4], respectively. ParBID was most effective at 2.5% noise level. Proposed method was applied to experimentally obtained images (slice thickness 1.2 mm). The results are shown in Fig.5. The fine shading and contrast of the images are well preserved in NC-BDnCNN as pointed by red arrows shown in (c) and (k). The application of ParBID further enhances contrast preservation. In general, PSNR tends to decrease when image structure preservation is increased, but in our study, both noise reduction and structure preservation were satisfied.

Conclusion

The effective noise reduction method that can improve the preservation of image structure is proposed and demonstrated. The application of parallel denoising process shows the possibility of further enhancing the preservation of image detail and structure.

Acknowledgements

This study was supported by JSPS KAKENHI(19K04423).