Wavelets and LPG-PCA for Image Denoising

In this chapter, a new image denoising approach is proposed. It combines two image denoising techniques. The first one is based on a wavelet transform (WT), and the second one is a two-stage image denoising by PCA (principal component analysis) with LPG (local pixel grouping). In this proposed approach, we first apply the first technique to the noisy image in order to obtain the first estimation version of the clean image. Then, we estimate the noise-level from the noisy image. This estimate is obtained by applying the third technique of noise estimation from noisy images. The third step of the proposed approach consists in using the first estimation of the clean image, the noisy image, and the estimate of the noise-level as inputs of the second image denoising system (LPG-PCA). A comparative study of the proposed technique and the two others denoising technique (one is based on WT and and the second is based on LPG-PCA), is performed. This comparative study used a number of noisy images, and the obtained results from PSNR (peak signal-to-noise ratio) and SSIM (structural similarity) computations show that the proposed approach outperforms the two other denoising approaches (the first one is based on WT and the second one is based on LPG-PCA)

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

Improvement of BM3D Algorithm and Employment to Satellite and CFA Images Denoising

This paper proposes a new procedure in order to improve the performance of block matching and 3-D filtering (BM3D) image denoising algorithm. It is demonstrated that it is possible to achieve a better performance than that of BM3D algorithm in a variety of noise levels. This method changes BM3D algorithm parameter values according to noise level, removes prefiltering, which is used in high noise level; therefore Peak Signal-to-Noise Ratio (PSNR) and visual quality get improved, and BM3D complexities and processing time are reduced. This improved BM3D algorithm is extended and used to denoise satellite and color filter array (CFA) images. Output results show that the performance has upgraded in comparison with current methods of denoising satellite and CFA images. In this regard this algorithm is compared with Adaptive PCA algorithm, that has led to superior performance for denoising CFA images, on the subject of PSNR and visual quality. Also the processing time has decreased significantly.Comment: 11 pages, 7 figur

Denoising with patch-based principal component analysis

One important task in image processing is noise reduction, which requires to recover image information by removing noise without loss of local structures. In recent decades patch-based denoising techniques proved to have a better performance than pixel-based ones, since a spatial neighbourhood can represent high correlations between nearby pixels and improve the results of similarity measurements. This bachelor thesis deals with denoising strategies with patch-based principal component analysis. The main focus lies on learning a new basis on which the representation of an image has the best denoising effect. The first attempt is to perform principal component analysis on a global scale, which obtains a basis that reflects the major variance of an image. The second attempt is to learn bases respectively over patches in a local window, so that more image details can be preserved. In addition, local pixel grouping is introduced to find similar patches in a local window. Due to the importance of sufficient samples in the principal component analysis transform, the third attempt is to search for more similar patches in the whole image by using a vantage point tree for space partitioning. In the part of implementation, parameter selection and time complexity are discussed. The denoising performance of different approaches is evaluated in terms of both PSNR value and visual quality.Eine der wichtigen Aufgaben in der Bildverarbeitung ist die Entrauschung, die erfordert Bildinformationen ohne Verlust lokaler Strukturen wiederzuherstellen. In den letzten Jahrzehnten hat es sich herausgestellt, dass Patch-basierte Verfahren eine bessere Leistung bei der Bildentrauschung haben als Pixel-basierte Verfahren. Der Grund liegt darin, dass eine räumliche Nachbarschaft die Korrelationen zwischen benachbarten Pixels repräsentiert und die Ergebnisse des Ähnlichkeitsmaß verbessern. In dieser Bachelorarbeit geht es um Entrauschungsstrategien mit der Patch-basierten Hauptkomponentenanalyse. Der Schwerpunkt liegt im Lernen einer neuen Basis, auf welcher die Representation eines Bildes den besten Entrauschungseffekt hat. Der erste Versuch ist, die Hauptkomponentenanalyse global durchzuführen und eine Basis zu erhalten, welche die Hauptvarianz eines Bildes reflektiert. Der zweite Versuch ist, mehrere Basen jeweils über Patches in einem lokalen Fenster zu lernen, um mehr Details zu behalten. Außerdem wird Local Pixel Grouping benutzt um ähnliche Patches in einem lokalen Fenster zu suchen. Die Hauptkomponentenanalyse ist wichtig dass genügend Samples vorhanden sind, daher werden im dritten Versuch weitere ähnliche Patches innerhalb des ganzen Bildes mithilfe von einem Vantage Point Baum gesucht. Im Teil der Implementierung wird über die Auswahl der Parameter und die Zeitkomplexität diskutiert. Die Entrauschungsleistung von unterschiedlichen Verfahren wird nach dem PSNR-Wert und der visuellen Qualität evaluiert

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

A note on patch-based low-rank minimization for fast image denoising

Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle component analysis (PCA) or singular value decomposition (SVD). Based on this idea, we propose a patch-based low-rank minimization method for image denoising. The main denoising process is stated in three equivalent way: PCA, SVD and low-rank minimization. Compared to recent patch-based sparse representation methods, experiments demonstrate that the proposed method is rather rapid, and it is effective for a variety of natural grayscale images and color images, especially for texture parts in images. Further improvements of this method are also given. In addition, due to the simplicity of this method, we could provide an explanation of the choice of the threshold parameter, estimation of PSNR values, and give other insights into this method.Comment: 4pages (two columns

Adaptive Non-Local Means using Weight Thresholding

Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses a patch-based approach to find similar regions within a search neighborhood and estimate the denoised pixel based on the weighted average of all the pixels in the neighborhood. All the pixels are considered for averaging, irrespective of the value of their weights. This thesis proposes an improved variant of the original NLM scheme, called Weight Thresholded Non-Local Means (WTNLM), by thresholding the weights of the pixels within the search neighborhood, where the thresholded weights are used in the averaging step. The key parameters of the WTNLM are defined using learning-based models. In addition, the proposed method is used as a two-step approach for image denoising. At the first step, WTNLM is applied to generate a basic estimate of the denoised image. The second step applies WTNLM once more but with different smoothing strength. Experiments show that the denoising performance of the proposed method is better than that of the original NLM scheme, and its variants. It also outperforms the state-of-the-art image denoising scheme, BM3D, but only at low noise levels (σ ≤ 80)