A Study on Clustering for Clustering Based Image De-Noising

In this paper, the problem of de-noising of an image contaminated with Additive White Gaussian Noise (AWGN) is studied. This subject is an open problem in signal processing for more than 50 years. Local methods suggested in recent years, have obtained better results than global methods. However by more intelligent training in such a way that first, important data is more effective for training, second, clustering in such way that training blocks lie in low-rank subspaces, we can design a dictionary applicable for image de-noising and obtain results near the state of the art local methods. In the present paper, we suggest a method based on global clustering of image constructing blocks. As the type of clustering plays an important role in clustering-based de-noising methods, we address two questions about the clustering. The first, which parts of the data should be considered for clustering? and the second, what data clustering method is suitable for de-noising.? Then clustering is exploited to learn an over complete dictionary. By obtaining sparse decomposition of the noisy image blocks in terms of the dictionary atoms, the de-noised version is achieved. In addition to our framework, 7 popular dictionary learning methods are simulated and compared. The results are compared based on two major factors: (1) de-noising performance and (2) execution time. Experimental results show that our dictionary learning framework outperforms its competitors in terms of both factors.Comment: 9 pages, 8 figures, Journal of Information Systems and Telecommunications (JIST

Poisson noise reduction with non-local PCA

Photon-limited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denoising methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio

Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a pre-collected dataset of example image patches, and then for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image non-local self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI

Adaptive Image Denoising by Targeted Databases

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a database that contains only relevant patches. We formulate the denoising problem as an optimal filter design problem and make two contributions. First, we determine the basis function of the denoising filter by solving a group sparsity minimization problem. The optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance. Improvement methods are proposed to enhance the patch search process. Second, we determine the spectral coefficients of the denoising filter by considering a localized Bayesian prior. The localized prior leverages the similarity of the targeted database, alleviates the intensive Bayesian computation, and links the new method to the classical linear minimum mean squared error estimation. We demonstrate applications of the proposed method in a variety of scenarios, including text images, multiview images and face images. Experimental results show the superiority of the new algorithm over existing methods.Comment: 15 pages, 13 figures, 2 tables, journa

Patch-based Denoising Algorithms for Single and Multi-view Images

In general, all single and multi-view digital images are captured using sensors, where they are often contaminated with noise, which is an undesired random signal. Such noise can also be produced during transmission or by lossy image compression. Reducing the noise and enhancing those images is among the fundamental digital image processing tasks. Improving the performance of image denoising methods, would greatly contribute to single or multi-view image processing techniques, e.g. segmentation, computing disparity maps, etc. Patch-based denoising methods have recently emerged as the state-of-the-art denoising approaches for various additive noise levels. This thesis proposes two patch-based denoising methods for single and multi-view images, respectively. A modification to the block matching 3D algorithm is proposed for single image denoising. An adaptive collaborative thresholding filter is proposed which consists of a classification map and a set of various thresholding levels and operators. These are exploited when the collaborative hard-thresholding step is applied. Moreover, the collaborative Wiener filtering is improved by assigning greater weight when dealing with similar patches. For the denoising of multi-view images, this thesis proposes algorithms that takes a pair of noisy images captured from two different directions at the same time (stereoscopic images). The structural, maximum difference or the singular value decomposition-based similarity metrics is utilized for identifying locations of similar search windows in the input images. The non-local means algorithm is adapted for filtering these noisy multi-view images. The performance of both methods have been evaluated both quantitatively and qualitatively through a number of experiments using the peak signal-to-noise ratio and the mean structural similarity measure. Experimental results show that the proposed algorithm for single image denoising outperforms the original block matching 3D algorithm at various noise levels. Moreover, the proposed algorithm for multi-view image denoising can effectively reduce noise and assist to estimate more accurate disparity maps at various noise levels