Adaptive Total Variation Regularization Research Articles

Hyperspectral sparse fusion using adaptive total variation regularization and superpixel-based weighted nuclear norm

Many recent studies have shown that the adaptive total variation regularization has the advantage of better preserving local features of images compared with the celebrated total variation regularization. On the other hand, the superpixel-based weighted nuclear norm can compensate for the shortcomings of the superpixel-based standard nuclear norm, assigning different weights to singular values and improving flexibility. Inspired by these two factors, we propose two new hyperspectral sparse fusion models related to the adaptive total variation regularization and superpixel-based weighted nuclear norm. Furthermore, we design the alternating direction method of multipliers (ADMM) to efficiently solve the proposed models, with complexity and convergence analyses. Experimental results demonstrate that the proposed methods outperform several state-of-the-art methods both numerically and visually.

High-resolution facial expression image restoration via adaptive total variation regularization for classroom learning environment

High-resolution facial expression image restoration via adaptive total variation regularization for classroom learning environment

Hyperspectral sparse unmixing based on a novel adaptive total variation regularization

Hyperspectral unmixing realizes the unmixing by determining the pure substances (endmembers) and their proportion (abundances) in the mixing pixels. Most of the previous sparse unmixing methods are effective in the case of high signal-to-noise ratio. However, these methods do not make full use of the spatial and spectral information of hyperspectral data, and their unmixing effect is not good enough in the case of high noise level. To solve this problem, in this paper, two new models are proposed. One is a hyperspectral sparse unmixing model using an adaptive total variation regularization (SU-ATV). Considering that different regions have different spatial structures, the adaptive total variation (ATV) regularization adaptively adjusts the horizontal difference and vertical difference of TV, which can better optimize the efficiency of TV to enhance the anti-noise performance. The other is an extended model (called WSU-ATV), where a spectral weight term is added to enhance the sparsity of abundance. To solve these two models, an alternating direction method of multipliers (ADMM) is presented. Experimental results on both synthetic data and real data show that the proposed models have better accuracy and anti-noise performance, compared with other related sparse unmixing methods. Besides, the WSU-ATV performs better than the SU-ATV owing to the spectral weight.

Hyperspectral Image Denoising With Weighted Nonlocal Low-Rank Model and Adaptive Total Variation Regularization

Hyperspectral image (HSI) is always corrupted by various types of noise during image capturing, such as Gaussian noise, stripe noise, deadline noise, impulse noise, and more. Such complicated noise significantly degrades imaging quality and thus limits the performance of downstream vision tasks. Current HSI denoising methods tackle this problem by modeling either the spectral-spatial prior of HSI or the noise characteristic of HSI, and few work consider the two aspects simultaneously. In this paper, we propose a new HSI denoising method by simultaneously modeling the HSI prior and the HSI noise characteristic. Specifically, we firstly utilize the non independent and identically distributed (non i.i.d.) mixture of Gaussian (MoG) assumption to characterize the complex noise, which corresponds to optimize a weighted fidelity function. Secondly, we exploit HSI’s non-local similarity and spatial-spectral correlation priors by applying non-local low rank model. Thirdly, we design an adaptive edge preserving total variation regularization term to characterize the non-local smooth property of HSI. Finally, we propose a new denoising model and develop effective ADMM algorithm to solve it. Extensive experiments on simulated data and real data substantiate the superiority of the proposed method beyond state-of-the-arts.

Adaptive total variation L1 regularization for salt and pepper image denoising

In this article, we propose an adaptive total variation (TV) regularization model for salt and pepper denoising in digital images. The adaptive TV denoising method is developed based on the general regularized image restoration model with L1 fidelity for handling salt and pepper noise model. An estimation for regularization parameter is also proposed based on the characteristics of the salt and pepper noise. We implement the proposed adaptive TV-L1 regularization model efficiently for image denoising using the primal dual gradient method. In the experiments, the full-reference image quality assessment metrics are used for evaluating denoising quality across various noise levels in different synthetic and real images. The denoising results are compared to other similar salt and pepper image denoising methods and our results indicate we obtain artifact free edge preserving restorations.

An adaptive algorithm for restoring image corrupted by mixed noise

Image denoising is one of the fundamental problems in image processing. Digital images are often contaminated by noise due to the image acquisition process under poor conditions. In this paper, we propose an effective approach to remove mixed Poisson-Gaussian noise in digital images. Particularly, we propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation. We also propose an instance of the alternating direction algorithm to solve the proposed denoising model as an optimization problem. The experiments on popular natural images demonstrate that our approach achieves superior accuracy than other recent state-of-the-art techniques.

A Rigid Motion Artifact Reduction Method for CT Based on Blind Deconvolution

In computed tomography (CT), artifacts due to patient rigid motion often significantly degrade image quality. This paper suggests a method based on iterative blind deconvolution to eliminate motion artifacts. The proposed method alternately reconstructs the image and reduces motion artifacts in an iterative scheme until the difference measure between two successive iterations is smaller than a threshold. In this iterative process, Richardson–Lucy (RL) deconvolution with spatially adaptive total variation (SATV) regularization is inserted into the iterative process of the ordered subsets expectation maximization (OSEM) reconstruction algorithm. The proposed method is evaluated on a numerical phantom, a head phantom, and patient scan. The reconstructed images indicate that the proposed method can reduce motion artifacts and provide high-quality images. Quantitative evaluations also show the proposed method yielded an appreciable improvement on all metrics, reducing root-mean-square error (RMSE) by about 30% and increasing Pearson correlation coefficient (CC) and mean structural similarity (MSSIM) by about 15% and 20%, respectively, compared to the RL-OSEM method. Furthermore, the proposed method only needs measured raw data and no additional measurements are needed. Compared with the previous work, it can be applied to any scanning mode and can realize six degrees of freedom motion artifact reduction, so the artifact reduction effect is better in clinical experiments.

Quantum Noise Removal in X-Ray Images with Adaptive Total Variation Regularization

Quantum Noise Removal in X-Ray Images with Adaptive Total Variation Regularization

Compressive Sensing Reconstruction of Correlated Images Using Joint Regularization

This letter proposes a novel compressive sensing reconstruction method for correlated images by using joint regularization, where a compensation-based adaptive total variation (CATV) regularization and a multi-image nonlocal low-rank (MNLR) regularization are included. In CATV, local weights are assigned to the residual values in the gradient domain so as to constrain the regularization strength at each pixel. In MNLR, the search of similar patches goes across different images so that both self-similarity and inter-image similarity are explored. Afterward, an efficient algorithm is proposed to solve the joint formulation, using a Split-Bregman-based technique. The effectiveness of the proposed approach is demonstrated with experiments on both multiview images and video sequences.

A spatially adaptive total variation regularization method for electrical resistance tomography

The total variation (TV) regularization method has been used to solve the ill-posed inverse problem of electrical resistance tomography (ERT), owing to its good ability to preserve edges. However, the quality of the reconstructed images, especially in the flat region, is often degraded by noise. To optimize the regularization term and the regularization factor according to the spatial feature and to improve the resolution of reconstructed images, a spatially adaptive total variation (SATV) regularization method is proposed. A kind of effective spatial feature indicator named difference curvature is used to identify which region is a flat or edge region. According to different spatial features, the SATV regularization method can automatically adjust both the regularization term and regularization factor. At edge regions, the regularization term is approximate to the TV functional to preserve the edges; in flat regions, it is approximate to the first-order Tikhonov (FOT) functional to make the solution stable. Meanwhile, the adaptive regularization factor determined by the spatial feature is used to constrain the regularization strength of the SATV regularization method for different regions. Besides, a numerical scheme is adopted for the implementation of the second derivatives of difference curvature to improve the numerical stability. Several reconstruction image metrics are used to quantitatively evaluate the performance of the reconstructed results. Both simulation and experimental results indicate that, compared with the TV (mean relative error 0.288, mean correlation coefficient 0.627) and FOT (mean relative error 0.295, mean correlation coefficient 0.638) regularization methods, the proposed SATV (mean relative error 0.259, mean correlation coefficient 0.738) regularization method can endure a relatively high level of noise and improve the resolution of reconstructed images.

Adaptive Total Variation Regularization Based SAR Image Despeckling and Despeckling Evaluation Index

We introduce a total variation (TV) regularization model for synthetic aperture radar (SAR) image despeckling. A dual-formulation-based adaptive TV (ATV) regularization method is applied to solve the TV regularization. The parameter adaptation of the TV regularization is performed based on the noise level estimated via wavelets. The TV-regularization-based image restoration model has a good performance in preserving image sharpness and edges while removing noises, and it is therefore effective for edge preserve SAR image despeckling. Experiments have been carried out using optical images contaminated with artificial speckles first and then SAR images. A despeckling evaluation index (DEI) is designed to assess the effectiveness of edge preserve despeckling on SAR images, which is based on the ratio of the standard deviations of two neighborhood areas of different sizes of a pixel. Experimental results show that the proposed ATV method can effectively suppress SAR image speckles without compromising the edge sharpness of image features according to both subjective visual assessment of image quality and objective evaluation using DEI.

Video super-resolution with registration-reliability regulation and adaptive total variation

In super-resolution that constructs a high-resolution (HR) image from a set of low-resolution (LR) reference images, it is crucial to align the LR reference images in order to efficiently exploit the pixels therein. However, due to the existence of complex local motion, ideal registration is difficult to acquire. In this paper, we present a robust video super-resolution scheme with registration-reliability regulation and content adaptive total variation regularization, which make the scheme resilient to registration failures. In order to handle ill-registered pixels, we propose a registration-reliability regulated data-fidelity term, which assigns smaller weights to the pixels with larger locally-averaged registration residuals. In addition, a content adaptive total variation based on structure tensor, which is used to estimate image local structures, is proposed to regularize the super-resolved images. The structure tensor is derived not only from the gradients of local patches but also the nonlocal similar patches. Experimental results show that the proposed scheme can remarkably improve both the objective and subjective quality of the video super-resolution results.

Supervised Spectral–Spatial Hyperspectral Image Classification With Weighted Markov Random Fields

This paper presents a new approach for hyperspectral image classification exploiting spectral-spatial information. Under the maximum a posteriori framework, we propose a supervised classification model which includes a spectral data fidelity term and a spatially adaptive Markov random field (MRF) prior in the hidden field. The data fidelity term adopted in this paper is learned from the sparse multinomial logistic regression (SMLR) classifier, while the spatially adaptive MRF prior is modeled by a spatially adaptive total variation (SpATV) regularization to enforce a spatially smooth classifier. To further improve the classification accuracy, the true labels of training samples are fixed as an additional constraint in the proposed model. Thus, our model takes full advantage of exploiting the spatial and contextual information present in the hyperspectral image. An efficient hyperspectral image classification algorithm, named SMLR-SpATV, is then developed to solve the final proposed model using the alternating direction method of multipliers. Experimental results on real hyperspectral data sets demonstrate that the proposed approach outperforms many state-of-the-art methods in terms of the overall accuracy, average accuracy, and kappa (k) statistic.

Adaptive total variation-based spectral deconvolution with the split Bregman method.

Spectroscopic data often suffer from common problems of band overlap and noise. This paper presents a maximum a posteriori (MAP)-based algorithm for the band overlap problem. In the MAP framework, the likelihood probability density function (PDF) is constructed with Gaussian noise assumed, and the prior PDF is constructed with adaptive total variation (ATV) regularization. The split Bregman iteration algorithm is employed to optimize the ATV spectral deconvolution model and accelerate the speed of the spectral deconvolution. The main advantage of this algorithm is that it can obtain peak structure information as well as suppress noise simultaneity. Simulated and real spectra experiments manifest that this algorithm can satisfactorily recover the overlap peaks as well as suppress noise and are robust to the regularization parameter.

An efficient algorithm for adaptive total variation based image decomposition and restoration

Abstract With the aim to better preserve sharp edges and important structure features in the recovered image, this article researches an improved adaptive total variation regularization and H−1 norm fidelity based strategy for image decomposition and restoration. Computationally, for minimizing the proposed energy functional, we investigate an efficient numerical algorithm—the split Bregman method, and briefly prove its convergence. In addition, comparisons are also made with the classical OSV (Osher–Sole–Vese) model (Osher et al., 2003) and the TV-Gabor model (Aujol et al., 2006), in terms of the edge-preserving capability and the recovered results. Numerical experiments markedly demonstrate that our novel scheme yields significantly better outcomes in image decomposition and denoising than the existing models.

Blind image deconvolution with spatially adaptive total variation regularization: erratum

Blind image deconvolution with spatially adaptive total variation regularization: erratum

Semiblind Image Deconvolution with Spatially Adaptive Total Variation Regularization

A semiblind image deconvolution algorithm with spatially adaptive total variation (SATV) regularization is introduced. The spatial information in different image regions is incorporated into regularization by using the edge indicator called difference eigenvalue to distinguish flat areas from edges. Meanwhile, the split Bregman method is used to optimize the proposed SATV model. The proposed algorithm integrates the spatial constraint and parametric blur-kernel and thus effectively reduces the noise in flat regions and preserves the edge information. Comparative results on simulated images and real passive millimeter-wave (PMMW) images are reported.

An Enhanced NAS-RIF Algorithm for Blind Image Restoration Based on Total Variation Regularization

In order to improve the quality of blind image restoration, we propose an algorithm which combines Non-negativity and Support constraint Recursive Inverse Filtering (NAS-RIF) and adaptive total variation regularization. In the proposed algorithm, the total variation regularization constraint term is added in the NAS-RIF algorithm cost function. The majorization-minimization approach and conjugate gradient iterative algorithm are adopted to improve the convergence speed. We do the simulation experiments for the blurred classic test image which is added additive random noise. Experimental results show that the restoration effect of our algorithm is better than the spatially adaptive Tikhonov regularization method and the NAS-RIF spatially adaptive regularization algorithm, while the value of improvement of signal to noise ratio (ISNR) has improved.

Blind image deconvolution with spatially adaptive total variation regularization

A blind deconvolution algorithm with spatially adaptive total variation regularization is introduced. The spatial information in different image regions is incorporated into regularization by using the edge indicator called difference eigenvalue to distinguish edges from flat areas. The proposed algorithm can effectively reduce the noise in flat regions as well as preserve the edge and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Comparative results on simulated and real degraded images are reported.

Adaptive total variation regularization based scheme for Poisson noise removal

To better preserve the edge features, this paper investigates an adaptive total variation regularization based variational model for removing Poisson noise. This edge‐preserving scheme comprises a spatially adaptive diffusivity coefficient, which adjusts the diffusion strength automatically. Compared with the classical total variation based one, numerical simulations distinctly indicate the superiority of our proposed strategy in maintaining the small details while denoising Poissonian image. Copyright © 2012 John Wiley & Sons, Ltd.