# Boosting of Denoising Effect with Fusion Strategy
## 1 Introduction
Based on the idea of nonlocal similarity and sparse representation of image patches, [PERSON] et al. introduced the nonlocally centralized sparse representation (NCSR) model [15] and the concept of sparse coding noise, thereby changing the objective of image denoising to suppressing the sparse coding noise. K-means clustering is applied to cluster the patches obtained from the given image into K clusters; then, a PCA sub-dictionary is adaptively learned for each cluster, leading to a more stable sparse representation. It is a fact that NCSR is efficient in capturing image details and adaptively representing them with a sparse description. However, since each image patch is considered as an independent unit of the sparse representation in the dictionary learning and sparse coding stages, ignoring the relationships among the patches can result in inaccurate sparse coding coefficients. There was a major leap in denoising performance with the revival of neural networks, which are trained on large collections of external noisy-clean image priors. [PERSON] and [PERSON] [16] presented gaussian mixture models (GMMs) using a gaussian mixture prior learned from a database of clean natural image patches to reproduce the latent image. PG prior based denoising (PGPD), a method developed based on GMMs, was proposed in [17] to exploit the non-local self-similarity of clean natural images. A convolutional neural network (CNN) for denoising was proposed in [18], where a five-layer convolutional network was specifically designed to synthesize training samples from abundantly available clean natural images. Subsequently, fully connected denoising auto-encoders [19] were suggested for image denoising. Nevertheless, the early CNN-based methods and the auto-encoders cannot compete with the benchmark BM3D [5] method. In [20], the plain multi-layer perceptron method is used to tackle image denoising with a multi-layer perceptron trained using training examples. This achieves a performance that is comparable with that of the BM3D method. [PERSON] and [PERSON] introduced the cascade of shrinkage fields (CSF) [21], which combines a random field-based model and half-quadratic optimization into a single learning framework to efficiently perform the denoising. [PERSON] et al. [22; 23] further presented the trainable nonlinear reaction diffusion (TNRD) method for image denoising problems. It learns the parameters from training data through a gradient descent inference approach. Both the CSF and TNRD show promise in narrowing the gap between denoising performance and computational efficiency. However, the specified forms of the priors adopted by these methods are limited with regard to capturing all the features related to image structure. Inspired by combining learning-based approaches with the traditional methods, [PERSON] et al. [24] defined a network known as the BM3D-Net by unrolling the computational pipeline of the classical BM3D algorithm into a CNN structure. It achieves competitive denoising results and significantly outperforms the traditional BM3D method. With regard to the development of deep CNNs, some prevalent deep CNN-based approaches are favorably compared to many other state-of-the-art methods both quantitatively and visually (e.g., recursively branched deconvolutional network (RBDN) [25], fast and flexible denoising convolutional neural network (FFDNet) [26], and residual learning of deep CNN (DnCNN) [27]). [PERSON] et al. [25] developed the RBDN for denoising as well as general image-to-image regression. Proposed by [PERSON] et al. in [26], by inputting an adjustable noise level map, the FFDNet is able to achieve visually convincing results on the trade-off between detail preservation and noise reduction with a single network model. Rather than outputting the denoised image \(x\) directly, in the case of the DnCNN, a residual mapping \(\vartheta\) is employed to estimate the noise existent in the input image, and the denoising result is \(x=y-\vartheta\).