We propose, in this letter, a new type of image denoising filter using a data analysis technique. We deal with pixels as data and extract the most dominant cluster from pixels in the filtering window. We output the centroid of the extracted cluster. We demonstrate that this graph-spectral filter can effectively reduce a mixture of Gaussian and random impulsive noise.

The influence of noise is an important problem on image acquisition and transmission stages. The traditional image denoising approaches only analyzing the pixels of local region with a moving window, which calculated by neighbor pixels to denoise. Recently, this research has been focused on the transform domain and feature space. Compare with the traditional approaches, the global multi-scale analyzing and unchangeable noise distribution is the advantage. Apparently, the estimation based methods can be used in transform domain and get better effect. This paper proposed a new approach to image denoising in orthonormal wavelet domain. In this paper, we adopt Stein's unbiased risk estimate (SURE) based method to denoise the low-frequency bands and the feature patches distance constraint (FPDC) method also be proposed to estimate the noise free bands in Wavelet domain. The key point is that how to divide the lower frequency sub-bands and the higher frequency sub-bands, and do interscale SURE and intrascale FPDC, respectively. We compared our denoising method with some well-known and new denoising algorithms, the experimental results show that the proposed method can give better performance and keep more detail information in most objective and subjective criteria than other methods.

This letter proposes a novel design approach for optimal contourlet filter banks based on the parametric 9/7 filter family. The Laplacian pyramid decomposition is replaced by optimal 9/7 filter banks with rational coefficients, and directional filter banks are activated using a pkva 12 filter in the contourlets. Moreover, based on this optimal 9/7 filter, we present an image denoising approach using a contourlet domain hidden Markov tree model. Finally, experimental results show that our approach in denoising images with texture detail is only 0.20 dB less compared to the method of Po and Do, and the visual quality is as good as for their method. Compared with the method of Po and Do, our approach has lower computational complexity and is more suitable for VLSI hardware implementation.

In this letter, we learned overcomplete filters to model rich priors of nature images. Our approach extends the Gaussian Scale Mixture Fields of Experts (GSM FOE), which is a fast approximate model based on Fields of Experts (FOE). In these previous image prior model, the overcomplete case is not considered because of the heavy computation. We introduce the assumption of quasi-orthogonality to the GSM FOE, which allows us to learn overcomplete filters of nature images fast and efficiently. Simulations show these obtained overcomplete filters have properties similar with those of Fields of Experts', and denoising experiments also show the superiority of our model.

Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multi-sensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the alpha and beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-determined (over-complete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for N-th order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multi-layer hierarchical NMF approach [3].

It is a very important and intriguing problem in digital image-processing to decompose an input image into intuitively convincible image-components such as a structure component and a texture component, which is an inherently nonlinear problem. Recently, several numerical schemes to solve the nonlinear image-decomposition problem have been proposed. The use of the nonlinear image-decomposition as a pre-process of several image-processing tasks will possibly pave the way to solve difficult problems posed by the classic approach of digital image-processing. Since the new image-processing approach via the nonlinear image-decomposition treats each separated component with a processing method suitable to it, the approach will successfully attain target items seemingly contrary to each other, for instance invisibility of ringing artifacts and sharpness of edges and textures, which have not attained simultaneously by the classic image-processing approach. This paper reviews quite recently developed state-of-the-art schemes of the nonlinear image-decomposition, and introduces some examples of the decomposition-and-processing approach.

Anomalous environmental electromagnetic (EM) radiation waves have been reported as the portents of earthquakes. Our study's goal is predicting earthquakes using EM radiation waves by detecting some anomalies. We have been measuring the Extremely Low Frequency (ELF) range EM radiation waves all over Japan. However, the recorded data contain signals unrelated to earthquakes. These signals, as noise, confound earthquake prediction efforts. In this paper, we propose an efficient method of global signal elimination and enhancement local signals using Independent Component Analysis (ICA). We evaluated the effectiveness of this method.

Obtaining the best linear unbiased estimator (BLUE) of noisy signals is a traditional but powerful approach to noise reduction. Explicitly computing the BLUE usually requires the prior knowledge of the noise covariance matrix and the subspace to which the true signal belongs. However, such prior knowledge is often unavailable in reality, which prevents us from applying the BLUE to real-world problems. To cope with this problem, we give a practical procedure for approximating the BLUE without such prior knowledge. Our additional assumption is that the true signal follows a non-Gaussian distribution while the noise is Gaussian.

In this paper, we consider the problem of bearing estimation for spatially distributed sources in unknown spatially-correlated noise. Assumed that the noise covariance matrix is centro-Hermitian, a differential denoising scheme is developed. Combined it with the classic DSPE algorithm, a differential denoising estimator is formulated. Its modified version is also derived. Exactly, the differential processing is first imposed on the covariance matrix of array outputs. The resulting differential signal subspace (DSS) is then utilized to weight array outputs. The noise components orthogonal to DSS are eliminated. Based on eigenvalue decomposition of the covariance matrix of weighted array outputs, the DSPE null spectrum is constructed. The asymptotic performance of the proposed bearing estimator is evaluated in a closed form. Moreover, in order to improve the performance of bearing estimation in case of low signal-to-noise ratio, a modified differential denoising estimator is proposed. Simulation results show the effectiveness of the proposed estimators under the low SNR case. The impacts of angular spread and number of sensors are also investigated.

Space-variant approaches subject to local image characteristics are useful in practical image restoration because many natural images are nonstationary. Motivated by the success of denoising approaches in the wavelet domain, we propose a region-adaptive restoration approach which adopts a wavelet denoising technique in flat regions after an under-regularized constrained least squares restoration. Experimental results verify that this approach not only improves image quality in mean square error but also contributes to ringing reduction.