Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to various degradations, such noises (random noise, HSI denoising), blurs (Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral and spatial downsample, HSI super-resolution). Previous HSI restoration methods are designed for one specific task only. Besides, most of them start from the 1-D vector or 2-D matrix models and cannot fully exploit the structurally spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this work, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which non-local similarity between spectral-spatial cubic and spectral correlation are simultaneously captured by 3-order tensors. Further, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently, and study its analytical solution. We also consider the exclusive stripe noise in HSI as the gross error by extending WLRTR to robust principal component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-arts in typical low level vision HSI tasks, including denoising, destriping, deblurring and super-resolution.
Image denoising is a test bed for the various technique. Consequently, numerous approaches for HSI denoising have been proposed @cite_18 @cite_21 @cite_76 . The spectral correlation and nonlocal self-similarity are two kinds of intrinsic characteristic underlying a HSI. Most of previous HSI denoising methods focus on the spectral correlation such as the wavelet methods @cite_6 , total variational methods @cite_79 , the low-rank matrix recovery methods @cite_38 @cite_87 @cite_62 @cite_46 , or the nonlocal self-similarity such as BM4D @cite_12 , HOSVD @cite_92 individually. Recently, @cite_94 firstly modeled them simultaneously in tensor format. However, the TDL @cite_94 is quite heuristic and short of a concise formulation, thus lacking of the flexibility to other HSI restoration tasks. Several tensor works @cite_52 @cite_31 @cite_70 followed the research line of @cite_94 , and model the sparsity of the core tensor coefficients in a principled manner. Interested readers could refer to @cite_99 for detailed background of HSI denoising. In this work, we further take the fine-grained intrinsic sparsity of the core tensor coefficients into consideration with the reweighting strategy, so as to better encode the structural correlation. Moreover, our WLRTR model can be well extended to other HSI issues.
@cite_99 @cite_38 @cite_18 @cite_62 @cite_31 @cite_87 @cite_70 @cite_92 @cite_21 @cite_52 @cite_6 @cite_79 @cite_94 @cite_46 @cite_76 @cite_12
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A framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called variational stationary noise remover. It can be interpreted both as a restoration method in a Bayesian framework and as a cartoon+texture decomposition method. In numerous denoising applications, the white noise assumption fails. For example, structured patterns such as stripes appear in the images. The model described here addresses these cases. Applications are presented with images acquired using different modalities: scanning electron microscope, FIB-nanotomography, and an emerging fluorescence microscopy technique called selective plane illumination microscopy. Hyperspectral images (HSIs) are often degraded by a mixture of various kinds of noise in the acquisition process, which can include Gaussian noise, impulse noise, dead lines, stripes, and so on. This paper introduces a new HSI restoration method based on low-rank matrix recovery (LRMR), which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. By lexicographically ordering a patch of the HSI into a 2-D matrix, the low-rank property of the hyperspectral imagery is explored, which suggests that a clean HSI patch can be regarded as a low-rank matrix. We then formulate the HSI restoration problem into an LRMR framework. To further remove the mixed noise, the “Go Decomposition” algorithm is applied to solve the LRMR problem. Several experiments were conducted in both simulated and real data conditions to verify the performance of the proposed LRMR-based HSI restoration method. In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented. The Magnetic Resonance (MR) Imaging technique has important applications in clinical diagnosis and scientific research. However, in practice the MR images are often corrupted by noise. Existing image denoising methods, mostly designed for natural image denoising do not take into account the multiple dimensionality of the 3D MR images, and are thus not suitable for 3D MR images denoising. In this paper, we present a novel noise reduction method for 3D MR images based on low-rank tensor approximation, considering both the non-local spatial self-similarity and the correlation across the slices of the 3D MR images. Specifically, for each exemplar 3D patch, similar 3D patches are first grouped to form a 4th order tensor. As the similar patches contain similar structures, the latent clear MR images can be recovered by a low-rank tensor approximation. To this end, an adaptive higher order singular value thresholding method is proposed. Experimental results on 3D MR images show that the proposed method can provide substantial improvements over the current state-of-the-art image denoising methods in terms of both objective metric and subjective visual quality. Patch-based low-rank models have shown effective in exploiting spatial redundancy of natural images especially for the application of image denoising. However, two-dimensional low-rank model can not fully exploit the spatio-temporal correlation in larger data sets such as multispectral images and 3D MRIs. In this work, we propose a novel low-rank tensor approximation framework with Laplacian Scale Mixture (LSM) modeling for multi-frame image denoising. First, similar 3D patches are grouped to form a tensor of d-order and high-order Singular Value Decomposition (HOSVD) is applied to the grouped tensor. Then the task of multiframe image denoising is formulated as a Maximum A Posterior (MAP) estimation problem with the LSM prior for tensor coefficients. Both unknown sparse coefficients and hidden LSM parameters can be efficiently estimated by the method of alternating optimization. Specifically, we have derived closed-form solutions for both subproblems. Experimental results on spectral and dynamic MRI images show that the proposed algorithm can better preserve the sharpness of important image structures and outperform several existing state-of-the-art multiframe denoising methods (e.g., BM4D and tensor dictionary learning). In this paper, a new noise reduction algorithm is introduced and applied to the problem of denoising hyperspectral imagery. This algorithm resorts to the spectral derivative domain, where the noise level is elevated, and benefits from the dissimilarity of the signal regularity in the spatial and the spectral dimensions of hyperspectral images. The performance of the new algorithm is tested on two different hyperspectral datacubes: an Airborne Visible Infrared Imaging Spectrometer (AVIRIS) datacube that is acquired in a vegetation-dominated site and a simulated AVIRIS datacube that simulates a geological site. The new algorithm provides signal-to-noise-ratio improvement up to 84.44 and 98.35 in the first and the second datacubes, respectively. The amount of noise included in a hyperspectral image limits its application and has a negative impact on hyperspectral image classification, unmixing, target detection, and so on. In hyperspectral images, because the noise intensity in different bands is different, to better suppress the noise in the high-noise-intensity bands and preserve the detailed information in the low-noise-intensity bands, the denoising strength should be adaptively adjusted with the noise intensity in the different bands. Meanwhile, in the same band, there exist different spatial property regions, such as homogeneous regions and edge or texture regions; to better reduce the noise in the homogeneous regions and preserve the edge and texture information, the denoising strength applied to pixels in different spatial property regions should also be different. Therefore, in this paper, we propose a hyperspectral image denoising algorithm employing a spectral-spatial adaptive total variation (TV) model, in which the spectral noise differences and spatial information differences are both considered in the process of noise reduction. To reduce the computational load in the denoising process, the split Bregman iteration algorithm is employed to optimize the spectral-spatial hyperspectral TV model and accelerate the speed of hyperspectral image denoising. A number of experiments illustrate that the proposed approach can satisfactorily realize the spectral-spatial adaptive mechanism in the denoising process, and superior denoising results are produced. As compared to the conventional RGB or gray-scale images, multispectral images (MSI) can deliver more faithful representation for real scenes, and enhance the performance of many computer vision tasks. In practice, however, an MSI is always corrupted by various noises. In this paper we propose an effective MSI denoising approach by combinatorially considering two intrinsic characteristics underlying an MSI: the nonlocal similarity over space and the global correlation across spectrum. In specific, by explicitly considering spatial self-similarity of an MSI we construct a nonlocal tensor dictionary learning model with a group-block-sparsity constraint, which makes similar full-band patches (FBP) share the same atoms from the spatial and spectral dictionaries. Furthermore, through exploiting spectral correlation of an MSI and assuming over-redundancy of dictionaries, the constrained nonlocal MSI dictionary learning model can be decomposed into a series of unconstrained low-rank tensor approximation problems, which can be readily solved by off-the-shelf higher order statistics. Experimental results show that our method outperforms all state-of-the-art MSI denoising methods under comprehensive quantitative performance measures. Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problem using L_1 norm and L_2 norm, which mainly deal with Laplacian and Gaussian noise, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP model by combining the penalized likelihood method with MoEP distributions. Such setting facilitates the learned LRMF model capable of automatically fitting the real noise through MoEP distributions. Each component in this mixture is adapted from a series of preliminary super-or sub-Gaussian candidates. An Expectation Maximization (EM) algorithm is also designed to infer the parameters involved in the proposed PMoEP model. The advantage of our method is demonstrated by extensive experiments on synthetic data, face modeling and hyperspectral image restoration. Hyperspectral imaging is beneficial in a diverse range of applications from diagnostic medicine, to agriculture, to surveillance to name a few. However, hyperspectral images often suffer from degradation such as noise and low resolution. In this paper, we propose an effective model for hyperspectral image (HSI) restoration, specifically image denoising and super-resolution. Our model considers three underlying characteristics of HSIs: sparsity across the spatial-spectral domain, high correlation across spectra, and non-local self-similarity over space. We first exploit high correlation across spectra and non-local self-similarity over space in the degraded HSI to learn an adaptive spatial-spectral dictionary. Then, we employ the local and non-local sparsity of the HSI under the learned spatial-spectral dictionary to design an HSI restoration model, which can be effectively solved by an iterative numerical algorithm with parameters that are adaptively adjusted for different clusters and different noise levels. In experiments on HSI denoising, we show that the proposed method outperforms many state-of-the-art methods under several comprehensive quantitative assessments. We also show that our method performs well on HSI super-resolution. We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d -dimensional patches are stacked together in a (d+1) -dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D “group.” The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction.