Split Bregman Iteration Algorithm Research Articles

Video Transmission Secrecy Improvement Based on Fractional Order Hyper Chaotic System

In the Digital World scenario, the confidentiality of information in video transmission plays an important role. Chaotic systems have been shown to be effective for video signal encryption. To improve video transmission secrecy, compressive encryption method is proposed to accomplish compression and encryption based on fractional order hyper chaotic system that incorporates Compressive Sensing (CS), pixel level, bit level scrambling and nucleotide Sequences operations. The measurement matrix generates by the fractional order hyper chaotic system strengthens the efficiency of the encryption process. To avoid plain text attack, the CS measurement is scrambled to its pixel level, bit level scrambling decreases the similarity between the adjacent measurements and the nucleotide sequence operations are done on the scrambled bits, increasing the encryption. Two stages are comprised in the reconstruction technique, the first stage uses the intra-frame similarity and offers robust preliminary retrieval for each frame, and the second stage iteratively improves the efficiency of reconstruction by integrating inter frame Multi Hypothesis (MH) estimation and weighted residual sparsity modeling. In each iteration, the residual coefficient weights are modified using a mathematical approach based on the MH predictions, and the Split Bregman iteration algorithm is defined to resolve weighted l1 regularization. Experimental findings show that the proposed algorithm provides good compression of video coupled with an efficient encryption method that is resistant to multiple attacks.

Split Bregman algorithm based on adaptive parameter for planar array sensor imaging

Planar array capacitance imaging is a visualization imaging technique based on the edge effect of electric fields. However, there are ill-posed problem and soft-field effects in the imaging process, which results in unstable and susceptible imaging. To address this issue, the inverse solution of planar array capacitive imaging system is transformed into an optimization problem with the approximate solution of linear-squares. A new cost function with total variation sparse reconstruction model is presented, which considers the sparsity of regularization operator to improve the stability of the inversion process. The adaptive split Bregman iterative algorithm is proposed to solve the inverse optimization problem. The computation is simplified by splitting the complex optimization problem into simple subproblems. The results show that the algorithm can obtain stable model updates, and numerical experiments prove the effectiveness and reliability of the algorithm.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging.

In this study, we present a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilize a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations are utilized to further improve the reconstruction quality. The proposed method is validated on both phantom and in vivo human brain T2 mapping data. Results suggest that the proposed method is superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimation accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

L2 Regularization Model with Removal of Gaussian Noise

In order to remove Gaussian noise from images, a Gaussian noise image restoration method based on the L2 norm regularization model was proposed. The L2 norm is selected as the data fidelity term and the gradient operator and wavelet frame as the regularization term to suppress the image ladder effect and protect the image edge details. Since the objective function of the model is a large convex function, the solving process is very tedious. The split Bregman iterative algorithm and alternate direction multiplier method are combined to restore the image. The experimental results show that show that the alternate direction multiplier method can effectively reduce the difficulty of solving the restoration model, and the image recovered by using this model has a higher peak signal-to-n ratio and better structural similarity and can get a clearer image.

Poststack Impedance Inversion With Geological Structure-Guided Total Variation Constraint

Impedance inversion is an effective method to estimate the properties of subsurface model from poststack seismic data. However, owing to the low quality of seismic data and other reasons, impedance inversion methods usually suffer from spatial discontinuities and low resolution. In order to overcome these problems, we have developed an impedance inversion method based on geological structure-guided total variation (GSGTV) constraint. Different from traditional TV constraint, GSGTV considers the spatial distribution of geological structures instead of imposing gradient constraints on impedance only in fixed directions (horizontal and vertical). Therefore, GSGTV not only retains the advantage of traditional TV that can preserve the edge of layer, but also overcomes the shortcomings of traditional TV that is only suitable for inverting block structures. This ensures that GSGTV can simultaneously improve the resolution and spatial continuity of the inversion result. The realization of impedance inversion method based on GSGTV constraint requires three steps. First, estimate the local structural orientation of the subsurface from seismic data. Then, construct GSGTV regularization term based on the local structural orientation. Finally, establish the inversion objective function and solve the function by the split-Bregman iterative algorithm. We compared the proposed method and the impedance inversion method based on traditional TV constraint with synthetic and real seismic data. The inversion results confirm that our method can improve the resolution and spatial continuity.

An Improved TV-Type Variational Regularization Method for Seismic Impedance Inversion

In this letter, we concern the acoustic impedance (AI) inversion from the known reflectivity based on the increasingly mature deconvolution techniques. For seismic data with the complicated geological structures, we first construct the regularization model for the AI inversion with the proposed regularizer consisting of the total variation (TV) seminorm and the Frobenius norm of the Hessian. Second, we develop the split Bregman (SB) iterative algorithm in the frequency domain for solving the proposed model. Finally, we verify the effectiveness of our proposed method via synthetic and field data. Experimental results demonstrate that our proposed method can not only preserve the lateral continuity and the impedance interfaces of the inverted AI section well, but also provide a higher resolution impedance section than the other related methods.

Efficient infrared imaging–blur kernel estimation with multi-scale feature learning for online learning video source

To enhance the infrared images resolution, a novel infrared imaging–blur kernel estimation model is proposed, which is based on multiscale deconvolution and total variation regularization. The blur kernel can be refined by the deconvolution algorithm with increasing scale level. Furthermore, the split Bregman iteration algorithm is used to optimize the proposed cost functions. The major novelty of the study is that the proposed model can recover the high-resolution image and an accurate blur kernel from a degraded image simultaneously. Qualitative and quantitative results on simulated and actual images demonstrate that the proposed method can estimate the infrared blur function accurately and produce high-resolution image. The enhanced infrared images can be applied to the application for the learning video quality improvement.

Seismic ground roll attenuation in DWT domain by split Bregman iteration algorithm

Noise reduction of seismic data is one of the most substantial steps in seismic signal processing. Goudarzi and Riahi presented wavelet domain ground roll analysis (WDGA), a technique based on the data. The results of this method showed a good improvement of the signal-to-noise ratio, but the WDGA did not work well in the data with a high level of random noise because this method uses a comparison-based search algorithm. This problem requires additional research to find a way to overcome this limitation. The wavelet domain split Bregman (WDSB) method presented in this paper is based on the use of the split Bregman algorithm in a discrete wavelet domain. The goal is to simultaneously use the capabilities of the F-K filter and the split Bregman iteration algorithm in the discrete wavelet domain, to overcome the problem of high levels of random noise in ground roll attenuation. The results of using WDSB for synthetic and real seismic data show improvement in ground roll attenuation while protecting seismic signals. The new algorithm is studied in time and wavelet domains.

Learning Image Profile Enhancement and Denoising Statistics Priors for Single-Image Super-Resolution

Single-image super-resolution (SR) has been widely used in computer vision applications. The reconstruction-based SR methods are mainly based on certain prior terms to regularize the SR problem. However, it is very challenging to further improve the SR performance by the conventional design of explicit prior terms. Because of the powerful learning ability, deep convolutional neural networks (CNNs) have been widely used in single-image SR task. However, it is difficult to achieve further improvement by only designing the network architecture. In addition, most existing deep CNN-based SR methods learn a nonlinear mapping function to directly map low-resolution (LR) images to desirable high-resolution (HR) images, ignoring the observation models of input images. Inspired by the split Bregman iteration (SBI) algorithm, which is a powerful technique for solving the constrained optimization problems, the original SR problem is divided into two subproblems: 1) inversion subproblem and 2) denoising subproblem. Since the inversion subproblem can be regarded as an inversion step to reconstruct an intermediate HR image with sharper edges and finer structures, we propose to use deep CNN to capture low-level explicit image profile enhancement prior (PEP). Since the denoising subproblem aims to remove the noise in the intermediate image, we adopt a simple and effective denoising network to learn implicit image denoising statistics prior (DSP). Furthermore, the penalty parameter in SBI is adaptively tuned during the iterations for better performance. Finally, we also prove the convergence of our method. Thus, the deep CNNs are exploited to capture both implicit and explicit image statistics priors. Due to SBI, the SR observation model is also leveraged. Consequently, it bridges between two popular SR approaches: 1) learning-based method and 2) reconstruction-based method. Experimental results show that the proposed method achieves the state-of-the-art SR results.

Learning Deep CNN Denoiser Priors for Depth Image Inpainting

Due to the rapid development of RGB-D sensors, increasing attention is being paid to depth image applications. Depth images play an important role in computer vision research. In this paper, we address the problem of inpainting for single depth images without corresponding color images as a guide. Within the framework of model-based optimization methods for depth image inpainting, the split Bregman iteration algorithm was used to transform depth image inpainting into the corresponding denoising subproblem. Then, we trained a set of efficient convolutional neural network (CNN) denoisers to solve this subproblem. Experimental results demonstrate the effectiveness of the proposed algorithm in comparison with three traditional methods in terms of visual quality and objective metrics.

Enhanced Non-Local Total Variation Model and Multi-Directional Feature Prediction Prior for Single Image Super Resolution.

It is widely acknowledged that single image super-resolution (SISR) methods play a critical role in recovering the missing high-frequencies in an input low-resolution image. As SISR is severely ill-conditioned, image priors are necessary to regularize the solution spaces and generate the corresponding high-resolution image. In this paper, we propose an effective SISR framework based on the enhanced non-local similarity modeling and learning-based multi-directional feature prediction (ENLTV-MDFP). Since both the modeled and learned priors are exploited, the proposed ENLTV-MDFP method benefits from the complementary properties of the reconstruction-based and learning-based SISR approaches. Specifically, for the non-local similarity-based modeled prior [enhanced non-local total variation, (ENLTV)], it is characterized via the decaying kernel and stable group similarity reliability schemes. For the learned prior [multi-directional feature prediction prior, (MDFP)], it is learned via the deep convolutional neural network. The modeled prior performs well in enhancing edges and suppressing visual artifacts, while the learned prior is effective in hallucinating details from external images. Combining these two complementary priors in the MAP framework, a combined SR cost function is proposed. Finally, the combined SR problem is solved via the split Bregman iteration algorithm. Based on the extensive experiments, the proposed ENLTV-MDFP method outperforms many state-of-the-art algorithms visually and quantitatively.

Adjusted Non-Local Regression and Directional Smoothness for Image Restoration

Image restoration (IR) problems are very important in many low-level vision tasks. Due to their ill-posed natures, image priors are widely used to regularize the solution spaces. Recently, patch-based non-local self-similarity has shown great potential in IR problems, leading to many effective non-local priors. Their performance largely depends on whether the non-local self-similarity of the underlying image can be fully exploited. However, most of these priors, including non-local regression (NLR), only utilize the center pixel of each patch to model the non-local feature, which is suboptimal. We propose an effective overlap-based non-local regression (ONLR) to fully exploit the non-local similar patches: first, the concept of overlap-based similar pixels group (OSPG) is introduced; second, for each pixel within an OSPG, the non-local weight is obtained via a novel similarity measurement method; third, based on the consistency assumption, the non-local fitting deviations (NLFDs) by using OSPGs are uniformly constrained. Because of the uniform constraints, the restoration may be poor in regions where OSPGs are not reliable. Consequently, a weighting scheme is proposed to measure the OSPG reliability, leading to a novel adjusted non-local regression (ANLR). In addition, the integral image technique (IIT) is adopted to speed up the similar patches search process. To further boost the ANLR, a local directional smoothness (DS) prior is proposed as a good complement of the non-local feature. Finally, a fast split Bregman iteration algorithm is designed to solve the ANLR-DS minimization problem. Extensive experiments on two typical IR problems, that is, image deblurring and super resolution, demonstrate the superiority of the proposed method compared to many state-of-the-art IR methods.

Iterative reconstruction algorithm for the inverse problems in electrical capacitance tomography

The electrical capacitance tomography (ECT) technology is a promising tomography technology that can image the distribution information of permittivity in a measurement region. The imaging algorithms play crucial roles in practical ECT image reconstruction problems. Different from previous numerical methods, this study proposes a novel cost function to model the ECT inverse problem, in which the L1-norm is used as the data fidelity to weaken the influence of the outliers contained in the capacitance data, the L1 regularization is introduced to enhance the sparseness of reconstructed objects, and the second order total variation (STV) regularization is used to weaken the staircasing effects caused by the first order total variation (FTV) regularization. The split Bregman iteration (SBI) algorithm that splits a complicated ECT imaging problem into several simpler sub-problems is developed to solve the proposed cost function effectively. The numerical simulation results show that the imaging algorithm proposed in this paper can reconstruct satisfactory results.

Group Sparsity based Sparse-Sampling CT Reconstruction.

Classical total variation (TV) based iterative re-construction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a novel computed tomography (CT) reconstruction method for the sparse-sampling problem called the group- sparsity regularization-based simultaneous algebraic reconstruction technique (GSR-SART). Group-based sparse representation, which utilizes the concept of a group as the basic unit of sparse representation instead of a patch, is introduced as the image domain prior regularization term to eliminate the over-smoothing effect. By grouping the nonlocal patches into different clusters with similarity measured by Euclidean distance, the sparsity and nonlocal similarity in a single image are simultaneously explored. The split Bregman iteration algorithm is applied to obtain the numerical scheme. Experimental results demonstrate that our method both qualitatively and quantitatively outperforms several existing reconstruction methods, including filtered back projection, expectation maximization, SART, and TV-based projections onto convex sets.

Few-view CT reconstruction with group-sparsity regularization.

Classical total variation-based iterative reconstruction algorithm is effective for the reconstruction of piecewise smooth image, but it causes oversmoothing effect for textured regions in the reconstructed image. To address this problem, this work presents a novel computed tomography reconstruction method for the few-view problem called the group-sparsity regularization-based simultaneous algebraic reconstruction technique (SART). Group-based sparse representation, which uses the concept of a group as the basic unit of sparse representation instead of a patch, is introduced as the image domain prior regularization term to eliminate the oversmoothing effect. By grouping the nonlocal patches into different clusters with similarity measured by Euclidean distance, the sparsity and nonlocal similarity in a single image are simultaneously explored. The split Bregman iteration algorithm is applied to obtain the numerical scheme. Experimental results demonstrate that our method both qualitatively and quantitatively outperforms several existing reconstruction methods, including filtered back projection, SART, total variation-based projections onto convex sets, and SART-based dictionary learning.

Reconstruction of Single Image from Multiple Blurry Measured Images.

The problem of blind image recovery using multiple blurry images of the same scene is addressed in this paper. To perform blind deconvolution, which is also called blind image recovery, the blur kernel and image are represented by groups of sparse domains to exploit the local and nonlocal information such that a novel joint deblurring approach is conceived. In the proposed approach, the group sparse regularization on both the blur kernel and image is provided, where the sparse solution is promoted by -norm. In addition, the reweighted data fidelity is developed to further improve the recovery performance, where the weight is determined by the estimation error. Moreover, to reduce the undesirable noise effects in group sparse representation, distance measures are studied in the block matching process to find similar patches. In such a joint deblurring approach, a more sophisticated two-step interactive process is needed in which each step is solved by means of the well-known split Bregman iteration algorithm, which is generally used to efficiently solve the proposed joint deblurring problem. Finally, numerical studies, including synthetic and real images, demonstrate that the performance of this joint estimation algorithm is superior to the previous state-of-the-art algorithms in terms of both objective and subjective evaluation standards. The recovery results of real captured images using unmanned aerial vehicles are also provided to further validate the effectiveness of the proposed method.

Robust Interpolation of DEMs From Lidar-Derived Elevation Data

Light detection and ranging (lidar)-derived elevation data are commonly subjected to outliers due to the boundaries of occlusions, physical imperfections of sensors, and surface reflectance. Outliers have a serious negative effect on the accuracy of digital elevation models (DEMs). To decrease the impact of outliers on DEM construction, we propose a robust interpolation algorithm of multiquadric (MQ) based on a regularized least absolute deviation (LAD) technique. The objective function of the proposed method includes a regularization-based smoothing term and an LAD-based fitting term, respectively, used to smooth noisy samples and resist the influence of outliers. To solve the objective function of the proposed method, we develop a simple scheme based on the split-Bregman iteration algorithm. Results from simulated data sets indicate that when sample points are noisy or contaminated by outliers, the proposed method is more accurate than the classical MQ and two recently developed robust algorithms of MQ for surface modeling. Real-world examples of interpolating 1 private and 11 publicly available airborne lidar-derived data sets demonstrate that the proposed method averagely produces better results than two promising interpolation methods including regularized spline with tension (RST) and gridded data-based robust thin plate spline (RTPS). Specifically, the image of RTPS is too smooth to retain terrain details. Although RST can keep subtle terrain features, it is distorted by some misclassified object points (i.e., pseudooutliers). The proposed method obtains a good tradeoff between resisting the effect of outliers and preserving terrain features. Overall, the proposed method can be considered as an alternative for interpolating lidar-derived data sets potentially including outliers.

Adaptive fractional-order total variation image restoration with split Bregman iteration

Alleviating the staircase artifacts for variation method and adjusting the regularization parameters adaptively with the characteristics of different regions are two main issues in image restoration regularization process. An adaptive fractional-order total variation l1 regularization (AFOTV-l1) model is proposed, which is resolved by using split Bregman iteration algorithm (SBI) for image estimation. An improved fractional-order differential kernel mask (IFODKM) with an extended degree of freedom (DOF) is proposed, which can preserve more image details and effectively avoid the staircase artifact. With the SBI algorithm adopted in this paper, fast convergence and small errors are achieved. Moreover, a novel regularization parameters adaptive strategy is given. Experimental results, by using the standard image library (SIL), the lung imaging database consortium and image database resource initiative (LIDC-IDRI), demonstrate that the proposed methods have better approximation, robustness and fast convergence performances for image restoration.

Data-driven multichannel seismic impedance inversion with anisotropic total variation regularization

Abstract Acoustic impedance (AI) inversion is a desirable tool to extract rock-physical properties from recorded seismic data. It plays an important role in seismic interpretation and reservoir characterization. When one of recursive inversion schemes is employed to obtain the AI, the spatial coherency of the estimated reflectivity section may be damaged through the trace-by-trace processing. Meanwhile, the results are sensitive to noise in the data or inaccuracies in the generated reflectivity function. To overcome the above disadvantages, in this paper, we propose a data-driven inversion scheme to directly invert the AI from seismic reflection data. We first explain in principle that the anisotropic total variation (ATV) regularization is more suitable for inverting the impedance with sharp interfaces than the total variation (TV) regularization, and then establish the nonlinear objective function of the AI model by using anisotropic total variation (ATV) regularization. Next, we solve the nonlinear impedance inversion problem via the alternating split Bregman iterative algorithm. Finally, we illustrate the performance of the proposed method and its robustness to noise with synthetic and real seismic data examples by comparing with the conventional methods.

Sparse approximation of fitting surface by elastic net

The goal of this paper is to develop a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant space and the balanced $$l_{1}, l_{2}$$ norm minimization (named elastic net). The elastic net can be solved efficiently by an adapted split Bregman iteration algorithm. Numerical experiments indicate that by choosing appropriate regularization parameters, the model can efficiently provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution.