# Improved Image Denoising Algorithm Based on Superpixel Clustering and Sparse Representation
## 1 Introduction  
As one of the most fundamental low-level vision problems, image denoising has been widely studied in computer vision, serving as the foundation and precondition for image processing, such as visual saliency detection, image segmentation, image classification, etc. In general, image denoising aims at recovering the clean image from the noise-corrupted image while preserving, as much as possible, the vital image features. During the past few decades, image denoising has drawn much research attention, resulting in a variety of efficient methods. Traditional image denoising methods include the median filter, the Gaussian filter, methods based on the total variation, wavelet threshold methods, etc. However, most of these methods frequently ignore the details of image features that include structure, texture, and edge features. To some extent, the ignorance of image details makes these methods suffer from many defects, comprising of over-smoothing, side effect, artifacts, loss of structure and texture features, ambiguousness of edges, etc. Motivated by the defects in traditional image denoising methods, significant progress has been made in recent years. As image denoising is typically an ill-posed problem, its solution might not be unique. Based on good learning image priors from noise-corrupted images or clean natural images, numerous methods have been proposed to obtain a better solution to the image denoising problem. In particular, nonlocal self-similarity (NSS) and sparsity are two popular image priors with great potential that lead to state-of-the-art performance. Based on the fact that local image details may appear multiple times across the entire image, NSS prompts a series of excellent algorithms for image denoising. The nonlocal means (NLM) [1] algorithm computed a noise-free pixel as the weighted average of pixels with similar neighborhoods in the fixed-size rectangle searching window, and achieved significant enhancement in denoising performance. Inspired by the success of NLM method, [PERSON] et al. [2] proposed a remarkable collaborative image denoising scheme, called block-matching and 3D filtering (BM3D). In this scheme, nonlocal similar patches were grouped into a 3D cube and collaborative filtering was conducted in the sparse 3D transform domain. The BM3D algorithm ranks among the best performing methods, yet its implementation is complex. Furthermore, the BM3D algorithm is based on classical fixed orthogonal dictionaries, thus lacking data-adaptability. Building on the principle of sparse and redundant representations [3], another category of methods has been developed, which can learn data-adaptive dictionaries for denoising. The K-SVD algorithm [4] has boosted denoising performance significantly. [PERSON] et al. [5] proposed the learned simultaneous sparse coding (LSSC) algorithm, which used nonlocal self-similarity (NSS) to improve sparse models with simultaneous sparse coding. In Reference [6], [PERSON] et al. clustered image into \(K\) groups to enhance the sparse representation via locally learned dictionaries, which took advantage of geometrical structure feature and the NSS prior in spatial domain. Subsequently, [PERSON] et al. [7] observed that the difference between the representation coefficients of original and degraded images was sparse, and added a restriction to ensure the minimization of the \(l_{1}\) norm for the difference. Thus, this model achieved good results in image denoising. By assuming that the matrix of nonlocal similar patches had a low-rank structure, the low-rank minimization based methods [8; 9] also achieved very competitive denoising results. [PERSON] et al. [10] later proposed a patch group (PG) based NSS prior learning scheme to learn explicit NSS models from natural images for high performance denoising, resulting in high peak signal to noise ratio (PSNR) measurements.