In this study, Bayesian image denoising, in which the prior distribution is assumed to be a Gaussian Markov random field (GMRF), is considered. Recently, an effective algorithm for Bayesian image denoising with a standard GMRF prior has been proposed, which can help implement the overall procedure and optimize its parameters in O(n)-time, where n is the size of the image. A new GMRF-type prior, referred to as a hierarchical GMRF (HGMRF) prior, is proposed, which is obtained by applying a hierarchical Bayesian approach to the standard GMRF prior; in addition, an effective denoising algorithm based on the HGMRF prior is proposed. The proposed HGMRF method can help implement the overall procedure and optimize its parameters in O(n)-time, as well as the previous GMRF method. The restoration quality of the proposed method is found to be significantly higher than that of the previous GMRF method as well as that of a non-local means filter in several cases. Furthermore, numerical evidence implies that the proposed HGMRF prior is more suitable for the image prior than the standard GMRF prior.

For image restoration, an image prior that is obtained from the morphological gradient has been proposed. In the field of mathematical morphology, the optimization of the structuring element (SE) used for this morphological gradient using a genetic algorithm (GA) has also been proposed. In this paper, we introduce a new image prior that is the sum of the morphological gradients and total variation for an image restoration problem to improve the restoration accuracy. The proposed image prior makes it possible to almost match the fitness to a quantitative evaluation such as the mean square error. It also solves the problem of the artifact due to the unsuitability of the SE for the image. An experiment shows the effectiveness of the proposed image restoration method.

Dai-Yuan (DY) conjugate gradient method is an effective method for solving large-scale unconstrained optimization problems. In this paper, a new DY method, possessing a spectral conjugate parameter βk, is presented. An attractive property of the proposed method is that the search direction generated at each iteration is descent, which is independent of the line search. Global convergence of the proposed method is also established when strong Wolfe conditions are employed. Finally, comparison experiments on impulse noise removal are reported to demonstrate the effectiveness of the proposed method.

In a local region of a color image, the color distribution often takes the form of a linear line in the RGB space. This property is called “Color Line” and we propose a denoising method based on this property. When a noise is added on an image, its color distribution spreads from the Color Line. The denoising is achieved by reducing the spread. In conventional methods, Color Line is assumed to be only a single line, but actual distribution takes various shapes such as a single line, two lines, and a plane and so on. In our method, we estimate the distribution in more detail using plane approximation and denoise each patch by reducing the spread depending on the Color Line types. In this way, we can achieve better denoising results than a conventional method.

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in O(n)-time, where n is the number of pixels in a given image. From the perspective of the order of the computational time, this is a state-of-the-art algorithm for the present problem setting. Moreover, the results of our numerical experiments we show our method is in fact effective in practice.

This paper proposes an image denoising method using singular value decomposition (SVD) with block-rotation-based operations in wavelet domain. First, we decompose a noisy image to some sub-blocks, and use the single-level discrete 2-D wavelet transform to decompose each sub-block into the low-frequency image part and the high-frequency parts. Then, we use SVD and rotation-based SVD with the rank-1 approximation to filter the noise of the different high-frequency parts, and get the denoised sub-blocks. Finally, we reconstruct the sub-block from the low-frequency part and the filtered the high-frequency parts by the inverse wavelet transform, and reorganize each denoised sub-blocks to obtain the final denoised image. Experiments show the effectiveness of this method, compared with relevant methods.

Mixed noise removal is a major problem in image processing. Different noises have different properties and it is required to use an appropriate removal method for each noise. Therefore, removal of mixed noise needs the combination of removal algorithms for each contained noise. We aim at the removal of the mixed noise composed of Additive White Gaussian Noise (AWGN) and Random-Valued Impulse Noise (RVIN). Many conventional methods cannot remove the mixed noise effectively and may lose image details. In this paper, we propose a new mixed noise removal method utilizing Direction Weighted Median filter (DWM filter) and Block Matching and 3D filtering method (BM3D). Although the combination of the DWM filter for RVIN and BM3D for AWGN removes almost all the mixed noise, it still loses some image details. We find the cause in the miss-detection of the image details as RVIN and solve the problem by re-detection with the difference of an input noisy image and the output by the combination. The re-detection process removes only salient noise which BM3D cannot remove and therefore preserves image details. These processes lead to the high performance removal of the mixed noise while preserving image details. Experimental results show our method obtains denoised images with clearer edges and textures than conventional methods.

In this paper, we introduce a new method to remove random-valued impulse noise in an image. Random-valued impulse noise replaces the pixel value at a random position by a random value. Due to the randomness of the noisy pixel values, it is difficult to detect them by comparison with neighboring pixels, which is used in many conventional methods. Then we improve the recent noise detector which uses a non-local search of similar structure. Next we propose a new noise removal algorithm by sparse representation using DCT basis. Furthermore, the sparse representation can remove impulse noise by using the neighboring similar image patch. This method has much more superior noise removal performance than conventional methods at images. We confirm the effectiveness of the proposed method quantitatively and qualitatively.

Using traditional single-layer dictionary learning methods, it is difficult to reveal the complex structures hidden in the hyperspectral images. Motivated by deep learning technique, a deep dictionary learning approach is proposed for hyperspectral image denoising, which consists of hierarchical dictionary learning, feature denoising and fine-tuning. Hierarchical dictionary learning is helpful for uncovering the hidden factors in the spectral dimension, and fine-tuning is beneficial for preserving the spectral structure. Experiments demonstrate the effectiveness of the proposed approach.

In this paper, an image prior based on soft-morphological filters and its application to image recovery are presented. In morphological image processing, a gray-scale image is represented as a subset in a three-dimensional space, which is spanned by spatial and intensity axes. Morphological opening and closing, which are basic operations in morphological image processing, respectively approximate the image subset and its complementary images as the unions of structuring elements that are translated in the three-dimensional space. In this study, the opening and closing filters are applied to an image prior to resolve the regularization problem of image recovery. When the proposed image prior is applied, the image is recovered as an image that has no noise component, which is eliminated by the opening and closing. However, the closing and opening filters are less able to eliminate Gaussian noise. In order to improve the robustness against Gaussian noise, the closing and opening filters are respectively approximated as soft-closing and soft-opening with relaxed max and min functions. In image recovery experiments, image denoising and deblurring using the proposed prior are demonstrated. Comparisons of the proposed prior with the existing priors that impose a penalty on the gradient of the intensity are also shown.

In this paper, we propose a novel multi-frame image denoising technique, which achieves the minimum variance of noise. Zero-mean and unknown variance white noise with an arbitrary distribution is considered in this paper. The proposed method consists of two parts. The first one is the estimation of the variance of noise for each image by considering the differences of all pairs of images. The second one is an actual denoising process in which the convex combination of all images with weight coefficients determined by the estimated variances is constructed. We also give an efficient algorithm by which we can obtain the same result by successive convex combinations. The efficacy of the proposed method is confirmed by computer simulations.

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.

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.