Non-blind image deblurring method by local and nonlocal total variation models

Compressive sensing (CS) has recently drawn considerable attentions in signal and image processing communities as a joint sampling and compression approach. Generally, the image CS reconstruction can be formulated as an optimization problem with a properly chosen regularization function based on image priors. In this paper, we propose an efficient image block compressive sensing (BCS) reconstruction method, which combine the best of group-based sparse representation (GSR) model and nonlocal total variation (NLTV) model to regularize the solution space of the image CS recovery optimization problem. Specifically, the GSR model is utilized to simultaneously enforce the intrinsic local sparsity and the nonlocal self-similarity of natural images, while the NLTV model is explored to characterize the smoothness of natural images on a larger scale than the classical total variation (TV) model. To efficiently solve the proposed joint regularized optimization problem, an algorithm based on the split Bregman iteration is developed. The experimental results demonstrate that the proposed method outperforms current state-of-the-art image BCS reconstruction methods in both objective quality and visual perception.

The total variation (TV) method for image deblurring is effective for sharpening image details in noisy images although this method tends to over-smooth the image details and inevitably results in staircase effects in smooth areas of the image. The nonlocal total variation (NLTV) method overcomes these drawbacks and retains fine details. However, it is not suitable for detecting similar patches and usually blurs edges in the image. Considering that the TV and NLTV are complementary, we propose a new local and nonlocal total variation (LNLTV) model. In this model, we first decompose the original image into a cartoon component and a detail component, then respectively apply the TV and NLTV to both components. To optimize the hybrid model, the Bregman iteration-based multivariable minimization (BIMM) method and the fast iteration-based multivariable minimization (FIMM) method are respectively employed to minimize the LNLTV energy function. The experimental results clearly demonstrate that the LNLTV model has better performance than some other state-of-the-art models with regard to evaluation indices and visual quality, and the FIMM method has a faster convergence rate and requires less time than the BIMM method.

This study presents an improved non‐local total variation (NLTV) model by using the block‐matching and three‐dimensional filtering (BM3D) algorithm for image denoising. First, the preprocessed image is obtained with the BM3D algorithm. Then, taking the place of the noisy image, the preprocessed image is used to construct the fidelity term of the energy functional and calculate the weight function in NLTV regularisation term. Finally, the energy functional is solved by the split Bregman algorithm. Experimental results demonstrate that the proposed model achieves better denoising performance than the original NLTV model in the visual appearance and objective indices, especially for the highly degenerated images. In addition, the proposed model can effectively suppress the appearance of the false information in the flat region, which overcomes the problem faced by the BM3D algorithm.

Filling dead pixels or eliminating unwanted things is typically preferred within the applications of remotely sensed images. In proposed article, a competent image imprinting technique is demonstrated to resolve this drawback, relied nonlocal total variation. Initially remotely sensed images are effected by ill posed inverse problems i.e. image destripping, image de-noising etc. So it is required to use regularization technique to makes these problems well posed i.e. NLTV method, which is the combination of nonlocal operators and total variation model. Actually this method can make use of the good features of non-local operators for textured images and total variation method in edge preserving for color images. To optimize the proposed variation model, an Ant Colony Optimization algorithm is used in order to get similarity with the original image. And evaluate the outcomes of proposed technique with the existing technique i.e. MNLTV optimized by Bregmanized-operator-splitting algorithm which is a prediction based method. The investigation of all outcomes confirms the efficacy of this rule.

Filling dead pixels or eliminating unwanted things is typically preferred within the applications of remotely sensed images. In proposed article, a competent image inpainting technique is demonstrated to resolve this drawback, relied Nonlocal total variation. Initially remotely sensed images are effected by ill posed inverse problems i.e. image destripping, image denoising etc. So it is required to use regularization technique to makes these problems well posed i.e. NLTV method, which is the combination of nonlocal operators and total variation model. Actually this method can make use of the good features of non local operators for textured images and total variation method in edge preserving for color images. To optimize the proposed variation model, an Ant Colony Optimization algorithm is used in order to get similarity with the original image. And evaluate the outcomes of proposed technique with the existing technique i.e. MNLTV optimized by Bregmanized-operator-splitting algorithm which is a prediction based method. The investigation of all outcomes confirms the efficacy of this rule.

In medical applications, computed tomography (CT) is widely used to evaluate various sample characteristics. However, image quality of CT reconstruction can be degraded due to artifacts. To propose and test a truncated total variation (truncation TV) model to solve the problem of large penalties for the total variation (TV) model. In this study, a truncated TV image denoising model in the fractional B-spline wavelet domain is developed to obtain the best solution. The method is validated by the analysis of CT reconstructed images of actual biological Pigeons samples. For this purpose, several indices including the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) and mean square error (MSE) are used to evaluate the quality of images. Comparing to the conventional truncated TV model that yields 22.55, 0.688 and 361.17 in PSNR, SSIM and MSE, respectively, using the proposed fractional B-spline-truncated TV model, the computed values of these evaluation indices change to 24.24, 0.898 and 244.98, respectively, indicating substantial reduction of image noise with higher PSNR and SSIM, and lower MSE. Study results demonstrate that compared with many classic image denoising methods, the new denoising algorithm proposed in this study can more effectively suppresses the reconstructed CT image artifacts while maintaining the detailed image structure.

An image denoising approach based on adaptive nonlocal total variation

The reasons of ineffectiveness of median filtering and its improved algorithm for eliminating the high-density salt-and-pepper noise are analyzed. A variational inpainting method is adopted to remove the high-density salt-and-pepper noise,and a inpainting model of Non-local Total Variation( NL-TV) based on the existing model of Total Variation( TV) is proposed in this article. In the NL-TV model based on the characteristics of salt-and-pepper noise( uniform distribution and the gray value of 0 or 255),we view the noise points as the lost or damaged points of an image to find the districts similar to the neighborhoods of noise points in an image,and then interpolate the noise points by taking the central pixel in a similar district as a new neighborhood of noise points. By this method,we transform the problem of image denoising into a problem of image restoration to remove the high-density noise. The experimental results show that the Peak Signal to Noise Ratios( PSNRs) are 22. 85 and 28. 77 after removing the noise for a color and gray-scale image with 90% of noise density,which is better than the results obtained by median filter and its improved algorithm in terms of the objective evaluation criteria. Using this model,we can effectively remove the high-density salt-and-pepper noise and restore the image details better,which provides a new approach to remove the high-density noise.

Imaging through turbid medium has many potential applications such as looking through clouds, seeing into seawater and observing through biological tissues. The transmission matrix (TM) method is one of the main imaging technologies that has potential in imaging of large targets. With aid of pre-measured TM, several optimization models are proposed to recover targets from speckle patterns, including ℓ₂ norm optimization model, sparse representation (SR) framework and total variation (TV) model. However, the solution of ℓ₂ norm optimization model contains large reconstruction noise, while the SR framework and TV model are two kinds of compressive sensing strategies, which require that the targets are sparse. In this paper, in order to image non-sparse targets and suppress the reconstruction noise, we apply the maximum entropy method (MEM) model to recover the target images from speckle patterns. Simulation results show that, for non-sparse target, the MEM model has better reconstruction performance under different noise levels compared with the TV model. For example, peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) of images reconstructed by MEM model at SNR=15 dB are comparable with those by TV model at SNR=35 dB.

Image restoration is a key step in the field of image processing. Total Variation (TV) model is widely applied in image denoising because it preserves edges and image details. However, TV model has some shortcomings, such as staircase artifacts and excessive smoothing of image texture area. Then we purpose a truncated L1-L2 Total Variational model, which is nonconvex and nonsmooth, for image restoration with impulse noise. In this proper, two algorithms, the alternating direction method of multiplier (ADMM) and the penalty-Gaussian Seidel type inertial proximal alternating linearized minimization (P-GiPALM), are designed to solve the nonconvex optimization. The subproblems are solved by the proximal difference-of -convex algorithm with extrapolation (pDCAe) and GiPALM with global convergence, respectively. The experimental results show that the new model has higher peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) values than those of median filter and the cutting-edge Cauchy denoising method.

The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed. In the existing works, the Grunwald–Letnikov fractional-order derivative is usually used, where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator. In this paper, a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation (tFoTV) model is proposed for image restoration. Hopefully, first any boundary condition can be used in the numerical experiments. Second, the accuracy of the reconstructed images by the tFoTV model can be improved. The alternating directional method of multiplier is applied to solve the tFoTV model. Its convergence is also analyzed briefly. In the numerical experiments, we apply the tFoTV model to recover images that are corrupted by blur and noise. The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio (PSNR) than the full fractional-order variation and total variation models. From the numerical results, we can also see that the tFoTV model is comparable with the total generalized variation (TGV) model in accuracy. In addition, we can roughly fix a fractional order according to the structure of the image, and therefore, there is only one parameter left to determine in the tFoTV model, while there are always two parameters to be fixed in TGV model.

A non-local vectorial total variational model for multichannel SAR image speckle suppression

The concept of computed tomography (CT) reconstruction from sparse-view data has been a considerable area of much research over the last several years. With the famous piecewise constant assumption, total variation (TV) model has been shown that it could be successfully applied to sparse-view CT reconstruction for producing accurate reconstructions. However, the resulting images from the traditional TV model based on local operators always meet the problems of smeared edges or staircase effects. In this paper, the TV minimization reconstruction model is extanded to a nonlocal TV (NLTV) model, using auxiliary variables and efficient split Bregman iterartive scheme, a reconstruction algorithm based on NLTV minimization has been developed. The proposed method shows excellent properties of edge preserving and smoothness preserving by using the nonlocal operators. Experimental results indicate that the proposed method could solve the above mentioned effects and reconstruct more accurate than the popular split Bregman-TV algorithm when applied to a sparse-view problem.

Several methods based on Total Variation (TV) have been proposed for Hyperspectral Image (HSI) denoising. However, the TV terms of these methods just use various l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norms and penalize image gradient magnitudes, having a negative influence on the preprocessing of HSI denoising and further HSI classification task. In this paper, a novel l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) is first introduced and analyzed for the HSI noise removal framework to preserve more information for classification. We propose a novel Tensor low-rank constraint and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) model in this paper. l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV directly controls the number of non-zero gradients and focuses on recovering the sharp image edges. The spectral-spatial information among all bands is exploited uniformly for removing mixed noise, which facilitates the subsequent classification after denoising. Including the Weighted Sum of Weighted Nuclear Norm (WSWNN) and the Weighted Sum of Weighted Tensor Nuclear Norm (WSWTNN), we propose two TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV-based algorithms, namely WSWNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV and WSWTNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV. The Alternating Direction Method of Multipliers (ADMM) and the Augmented Lagrange Multiplier (ALM) are employed to solve the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model and TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model, respectively. In both simulated and real data, the proposed models achieve superior performances in mixed noise removal of HSI. Especially, HSI classification accuracy is improved more effectively after denoising by the proposed TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV method.