# Boosting of Denoising Effect with Fusion Strategy
## 1 Introduction  
Digital images are often corrupted by noise during the acquisition or transmission of the images [1], rendering these images unsuitable for vision applications such as remote sensing and object recognition. Therefore, image denoising is a fundamental preprocessing step that aims at suppressing noise and reproducing the latent high quality image with fine image edges, textures, and rich details. A corrupted noisy image can be generally described as:  
\[y=x+v \tag{1}\]  
where the column vector \(x\) denotes the original clean image, and the \(v\) denotes the additive noise. There are many possible solutions for \(x\) of a noisy image \(y\) because the noise \(v\) is unknown. This is a fact that encourages scholars to continue seeking for new methods to achieve better denoising results. Various image denoising studies assume \(v\) to be additive white gaussian noise (AWGN). Considering that AWGN is stationary and uncorrelated among pixels, we made the same assumption for this study. Denoising methods can be classified into two types [2], internal methods and external ones. The internal methods denoise an image patch using other noisy image patches within the noisy image, whereas the external methods denoise a patch using externally clean image patches. In the past several years, the internal sparsity and the self-similarity of images were usually utilized to achieve betterdenoising performance. Non-local Means (NLM), proposed by [PERSON] et al. [3; 4], is the first filter that utilizes the non-local self-similarity in images. NLM obtains a denoised patch by first finding similar patches and obtaining their weighted average. Because searching for similar patches in various noise levels may be computationally impractical, typically, only a small neighborhood of the patch is considered for searching possible matches. BM3D [5], a characteristic benchmark method, builds on the strategy of NLM by grouping similar patches together, and suggests a two-step denoising algorithm. First, the input image is roughly denoised. Then, the denoising is refined by collecting similar patches to accomplish a collaborative filtering in the transform domain. This two-step process contributes to the effectiveness of the BM3D, making it a benchmark denoising algorithm. The nuclear norm minimization (NNM) method was proposed in [6] for video denoising; nevertheless, it was greatly restricted by its capability and flexibility in handling many practical denoising problems. In [7], [PERSON] et al. presented weighted nuclear norm minimization (WNNM). This was a low rank image denoising approach based on non-local self-similarity; however, it suppressed the low rank parts and shrank the reconstructed data. The K-SVD [8] denoising utilizes the sparse and redundant representations of an over-complete learned dictionary to produce a high-quality denoised image. Such a dictionary was initially learned from a large number of clean images. Later, it was directly learned from the noisy image patches [9]. Motivated by the idea of similar image patches sharing similar subdictionaries, [PERSON] et al. [10] proposed the K-LLD. Instead of learning a single over-complete dictionary for an entire image, K-LLD first performs a clustering step based on the patches using the local weight function presented in [11]. Then, it separately finds the most optimal dictionary for each cluster to denoise the patches from each cluster. Similarly, the authors of learned simultaneous sparse coding (LSSC) [12; 13] exploit self-similarities of image patches combined with sparse coding to further improve the performance of image denoising methods based on dictionary learning using a single dictionary. Taking advantage of the noise properties of local patches and different channels, a scheme called trilateral weight sparse coding (TWSC) was proposed in [14]. In this model, the noise statistics and sparsity priors of images are adaptively characterized by two weight matrices.