Split Bregman Iteration Research Articles

Modification of TV-ROF denoising model based on Split Bregman iterations

Minimizing variational models by means of (un)constrained optimization algorithms is a well-known approach for dealing with the image denoising problem. In this paper, we propose a modification of the widely explored TV-ROF model named H-TV-ROF, in which a penalty term based on higher order derivatives is added. A Split Bregman iterative scheme is used to solve the proposed model and its convergence is proved. The performance of the new algorithm is analized and compared with TV-ROF on a set of numerical experiments.

Variational framework for low-light image enhancement using optimal transmission map and combined [formula omitted] and [formula omitted]-minimization

This paper presents a novel variational framework for low-light image enhancement. The proposed enhancement algorithm simultaneously performs brightness enhancement and noise reduction using a variational optimization. An edge-preserved noise reduction is performed by minimizing the total variation constraint term in the energy function. In addition, the proposed method estimates the optimal transmission map to restore the low-light image by minimizing the ℓ2-norm smoothness and data-fidelity terms. To minimize the proposed energy functional, the proposed method splits the ℓ1-derivative term under the split Bregman iteration framework. The performance of the proposed method is evaluated using both simulated and natural low-light images. Experimental results show that the proposed enhancement method can significantly improve the quality of the low-light images without noise amplification.

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.

Non-local total bounded variation scheme for multiple-coil magnetic resonance image restoration

In this paper, we design a variational model for restoring multiple-coil magnetic resonance images (MRI) corrupted by non-central Chi distributed noise. The energy functional corresponding to the restoration problem is derived using the maximum a posteriori (MAP) estimator. Optimizing this functional yields the solution, which corresponds to the restored version of the image. The non-local total bounded variation prior is being used as the regularization term in the functional derived using the MAP estimation process. Further, the split-Bregman iteration scheme is being followed for fast numerical computation of the model. The results are compared with the state of the art MRI restoration models using visual representations and statistical measures.

Texture image prior for SAR image super resolution based on total variation regularization using split Bregman iteration

ABSTRACTIn this article, we propose a total variation (TV) regularization approach for the reconstruction of super-resolution synthetic aperture radar (SAR) image based on gradient profile prior or other texture image prior in the maximum a posteriori framework. We also design a novel super-resolution reconstruction algorithm via split Bregman iteration with the known degradation matrix, thereby enhancing the resolution of the SAR image. The parameter adaptation of the TV regularization is performed based on the high-resolution (HR) SAR image at each step. Several evaluation indices are tested on SAR images for objective assessment of the performance of SAR image super-resolution reconstruction. This computationally efficient algorithm is robust to noise in SAR scenes in HR image estimation. Experimental results show that the proposed split Bregman super-resolution approach can effectively avoid the speckle noise generated due to some strange textures and has good effect of noise suppression, while effectively maintaining the SAR image content, the structure of the SAR image is more apparent. Additionally, the experimental results on real SAR scenes also demonstrate the effectiveness of the proposed algorithm and demonstrate its superiority to other super-resolution algorithms.

Adaptive Bregmanized total variation model for mixed noise removal

To solve the problem of the staircase effect and removing mixed noise, including Gaussian and salt and pepper noise, which can occur during image formation and transmission, a total variation-based denoising model using an edge detection function is proposed. Moreover, an improved split Bregman iteration method is used to solve the nonlinear problem. The results of comparative experiments demonstrate that the proposed model removes Gaussian and salt and pepper noise while maintaining detailed features.

Least absolute deviation-based robust support vector regression

To suppress the influence of outliers on function estimation, we propose a least absolute deviation (LAD)-based robust support vector regression (SVR). Furthermore, an efficient algorithm based on the split-Bregman iteration is introduced to solve the optimization problem of the proposed algorithm. Both artificial and benchmark datasets are employed to compare the performance of the proposed algorithm with those of least squares SVR (LS-SVR), and two weighted versions of LS-SVR with the weight functions of Hampel and Logistic, respectively. Experiments demonstrate the superiority of the proposed algorithm.

Video Compressive Sensing Reconstruction via Reweighted Residual Sparsity

The compressive sensing (CS) theory indicates that robust reconstruction of signals can be obtained from far fewer measurements than those required by the Nyquist–Shannon theorem. Thus, CS has great potential in video acquisition and processing, considering that it makes the subsequent complex data compression unnecessary. In this paper, we propose a novel algorithm for effectively reconstructing videos from CS measurements. The algorithm comprises double phases, of which the first phase exploits intra-frame correlation and provides good initial recovery for each frame, and the second phase iteratively enhances reconstruction quality by alternating interframe multihypothesis (MH) prediction and sparsity modeling of residuals in a weighted manner. The weights of residual coefficients are updated in each iteration using a statistical method based on the MH predictions. These procedures are performed in the unit of overlapped patches such that potential blocking artifacts can be effectively suppressed through averaging. In addition, we devise an effective scheme based on the split Bregman iteration algorithm to solve the formulated weighted ${\ell }_{1}$ minimization problem. The experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art methods in both objective and subjective reconstruction quality.

Total variation based DCE-MRI decomposition by separating lesion from background for time-intensity curve estimation.

This study aims to obtain the accurate time intensity curve (TIC) of a dynamic contrast-enhanced magnetic resonance image (DCE-MRI) by eliminating the normal tissue enhancement and obtaining pure lesion information. The TIC of DCE-MRI is sometimes distorted because of the influence of normal tissue. In this paper, a new tracer-kinetic modeling based on total variation (DC-TV) is proposed to address this problem by decomposing the DCE-MRI into the normal tissue image and the lesion image. As TIC generation is not standardized and a credible program is expected, an accurate TIC generation is presented in this paper. We propose a new tracer-kinetic model DC-TV to decompose the lesion region in breast DCE-MRIs. The original image is decomposed into a normal tissue image and a lesion image to obtain the pure lesion enhancement information. The acquired lesion images are smooth and correspond to the diffusion of the contrast agent in the lesion. The normal tissue image sequences are stable and correspond to the enhanced normal tissue. To speed up the computational process of our convergent algorithm, the split Bregman iteration algorithm is applied. To compare the algorithm results, images generated by decomposed methods without normal tissue constraint based on total variation are compared with those generated by our method. The performance of the proposed method is evaluated by the correlation of normal tissue images with the lesion classification accuracy of lesion images. Ninety-eight lesions, including 40 benign and 58 malignant, are evaluated. The dataset includes various typical pathologies of the breast such as invasive ductal carcinoma, ductal carcinoma in situ, tubular carcinoma, phyllodes tumor, hyperplasia, and fibroadenoma, among others. The area under the ROC for the pure lesion enhancement images acquired by DC-TV is greater than that acquired by the original DCE-MRIs. The pure enhancement information from the original breast DCE-MRI lesions can be successfully obtained using our DC-TV. The TICs based on the acquired pure enhancement information closely conform to three-time-point model, which is a classic diagnosis rule. The experiment shows that DC-TV provide a credible TIC generation program.

Pixel-wise partial volume effects correction on arterial spin labeling magnetic resonance images

Arterial spin labeling is a recently emerging imaging modality in functional magnetic resonance, and it is widely acknowledged to be effective in directly measuring the cerebral blood flow of patients while being scanned, which makes it a promising indicator in contemporary dementia disease diagnosis studies. However, partial volume effects mainly caused by signal cross-contamination due to pixel heterogeneity and limited spatial resolution of the arterial spin labeling scanning protocol often prevent the cerebral blood flow from being accurately measured. In order to correct the partial volume effects, contemporary studies usually rely on neighboring pixles to solve indefinite equations of partial volume correction, which makes shortcomings of blurring and brain tissue details loss inevitable in their correction outcomes. In this study, a novel pixel-wise correction method is proposed to tackle partial volume effects in arterial spin labeling images. The main idea is to formalize the correction problem as a series of quadratic programming sub-problems using split-Bregman iterations, then formulate each sub-problem via the regularization of least absolute shrinkage and selection operator, and finally solve the regularization sub-problem via the fast proximal gradient descent approach. A real-patients database composed of 360 demented patients is incorporated for experimental evaluation of the pixel-wise method. Extensive experiments and comprehensive statistical analysis are carried out to demonstrate the superiority of the pixel-wise method with comparisons towards the popular region-based method. Promising results are reported from the statistical point of view.

Seismic acoustic impedance inversion with multi-parameter regularization

Most acoustic impedance sparse inversion methods include two parts: reflectivity inversion and extraction of acoustic impedance from reflectivity. This being the case, the acoustic impedance is easily affected by reflectivity and the value of acoustic impedance at time t = 0, thus may become inaccurate. In this paper, we propose a seismic acoustic impedance inversion method with multi-parameter regularization. In our method, the acoustic impedance is calculated directly from objective functions to ensure the stability and accuracy of results. In addition, the total variation regularization, L1 norm constraint, and initial model constraint are used to make the inversion results better accordant with a priori geological information. Moreover, we use multi-trace inversion to reflect the spatial and temporal correlation of the data. Since the objective function contains several different types of regularization term, we have developed an algorithm based on split Bregman iteration to calculate it. The inversion results of theoretical model and field data show that the proposed method has high inversion precision, strong anti-noise ability and good performance on stratigraphy delineation.

A content-based recommendation algorithm for learning resources

Automatic multimedia learning resources recommendation has become an increasingly relevant problem: it allows students to discover new learning resources that match their tastes, and enables the e-learning system to target the learning resources to the right students. In this paper, we propose a content-based recommendation algorithm based on convolutional neural network (CNN). The CNN can be used to predict the latent factors from the text information of the multimedia resources. To train the CNN, its input and output should first be solved. For its input, the language model is used. For its output, we propose the latent factor model, which is regularized by L 1-norm. Furthermore, the split Bregman iteration method is introduced to solve the model. The major novelty of the proposed recommendation algorithm is that the text information is used directly to make the content-based recommendation without tagging. Experimental results on public databases in terms of quantitative assessment show significant improvements over conventional methods. In addition, the split Bregman iteration method which is introduced to solve the model can greatly improve the training efficiency.

A general framework of piecewise-polynomial Mumford–Shah model for image segmentation

ABSTRACTA new general framework of piecewise-polynomial Mumford–Shah model is proposed. In terms of the fidelity term, we use piecewise polynomials to approximate the inner and outer regions of the contour of the objective image. For more accurate approximation of the image, the proposed model has no constraint on the regularization term for polynomials. Moreover, we apply the anisotropic control to drive the initial contour to the desirable position. The proposed model generalizes the well-known Chan–Vese model and improves Vese's model, which is almost the simplest framework to apply piecewise polynomials to approximate the original Mumford–Shah model. Instead of solving the Euler–Lagrange equation by evolution implementation, we utilize the split Bregman iteration, which is shown to be a fast algorithm. Experimental results demonstrate that the proposed model has more desirable performance in terms of segmentation accuracy, efficiency and robustness, compared with several other variational models in addressing some challenging segmentation scenarios.

A Unidirectional Total Variation and Second-Order Total Variation Model for Destriping of Remote Sensing Images

Remote sensing images often suffer from stripe noise, which greatly degrades the image quality. Destriping of remote sensing images is to recover a good image from the image containing stripe noise. Since the stripes in remote sensing images have a directional characteristic (horizontal or vertical), the unidirectional total variation has been used to consider the directional information and preserve the edges. The remote sensing image contaminated by heavy stripe noise always has large width stripes and the pixels in the stripes have low correlations with the true pixels. On this occasion, the destriping process can be viewed as inpainting the wide stripe domains. In many works, high-order total variation has been proved to be a powerful tool to inpainting wide domains. Therefore, in this paper, we propose a variational destriping model that combines unidirectional total variation and second-order total variation regularization to employ the directional information and handle the wide stripes. In particular, the split Bregman iteration method is employed to solve the proposed model. Experimental results demonstrate the effectiveness of the proposed method.

Electrical Capacitance Tomography Measurement of the Migration of Ice Frontal Surface in Freezing Soil

Abstract The tracking of the migration of ice frontal surface is crucial for the understanding of the underlying physical mechanisms in freezing soil. Owing to the distinct advantages, including non-invasive sensing, high safety, low cost and high data acquisition speed, the electrical capacitance tomography (ECT) is considered to be a promising visualization measurement method. In this paper, the ECT method is used to visualize the migration of ice frontal surface in freezing soil. With the main motivation of the improvement of imaging quality, a loss function with multiple regularizers that incorporate the prior formation related to the imaging objects is proposed to cast the ECT image reconstruction task into an optimization problem. An iteration scheme that integrates the superiority of the split Bregman iteration (SBI) method is developed for searching for the optimal solution of the proposed loss function. An unclosed electrodes sensor is designed for satisfying the requirements of practical measurements. An experimental system of one dimensional freezing in frozen soil is constructed, and the ice frontal surface migration in the freezing process of the wet soil sample containing five percent of moisture is measured. The visualization measurement results validate the feasibility and effectiveness of the ECT visualization method

Image decomposition‐based blind image deconvolution model by employing sparse representation

Conventional blind restoration methods often take consideration of images as a whole. However, an image may have different types of components, and each component has different morphology and properties. Using one model only can capture one part of images effectively, but fail to represent the others; the processing results by using conventional methods would lose some important features. In this study, a new sparse prior-based blind image deconvolution model has been proposed by employing commonly considered image decomposition strategy which separates an image into cartoon (piecewise-smooth part) and texture (the oscillating pattern part). On the basis of the different properties of cartoon and texture, it, respectively, regularises the texture with the sparsity of discrete cosine transform domain, and the cartoon with a combined term including framelet-domain-based sparse prior and a quadratic regularisation. Then a double alternating split Bregman iteration is proposed to address the proposed minimisation problem. It has been demonstrated that images can be recovered with high quality and more abundant features by authors’ proposed algorithm than other popular deblurring methods.

Simultaneous deghosting and wavelet estimation via blind deconvolution

Seismic deconvolution and deghosting are common methods for increasing the temporal resolution of marine seismic data. In this paper, we employ the advantages of multichannel blind deconvolution technique to obtain a deghosting algorithm for source and receiver side ghost elimination. The advantage of the proposed algorithm is two fold: first, it uses the correlation between the information contained in neighboring traces to stabilize the deghosting process while deconvolving the data in a blind fashion. Second, an estimation of the source wavelet is simultaneously provided by the inversion process. A fast algorithm is provided to solve the inverse problem by using the split Bregman iteration. Numerical results from simulated and field seismic data confirm the effectiveness of the proposed algorithm for automatic deghosting and deconvolution of marine data while being able to recover complex mixed-phase source wavelets.

Compressed sensing image reconstruction via adaptive sparse nonlocal regularization

Compressed sensing (CS) has been successfully utilized by many computer vision applications. However,the task of signal reconstruction is still challenging, especially when we only have the CS measurements of an image (CS image reconstruction). Compared with the task of traditional image restoration (e.g., image denosing, debluring and inpainting, etc.), CS image reconstruction has partly structure or local features. It is difficult to build a dictionary for CS image reconstruction from itself. Few studies have shown promising reconstruction performance since most of the existing methods employed a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) as the dictionary, which lack the adaptivity to fit image local structures. In this paper, we propose an adaptive sparse nonlocal regularization (ASNR) approach for CS image reconstruction. In ASNR, an effective self-adaptive learning dictionary is used to greatly reduce artifacts and the loss of fine details. The dictionary is compact and learned from the reconstructed image itself rather than natural image dataset. Furthermore, the image sparse nonlocal (or nonlocal self-similarity) priors are integrated into the regularization term, thus ASNR can effectively enhance the quality of the CS image reconstruction. To improve the computational efficiency of the ASNR, the split Bregman iteration based technique is also developed, which can exhibit better convergence performance than iterative shrinkage/thresholding method. Extensive experimental results demonstrate that the proposed ASNR method can effectively reconstruct fine structures and suppress visual artifacts, outperforming state-of-the-art performance in terms of both the PSNR and visual measurements.

Second-order TGV model for Poisson noise image restoration.

Restoring Poissonian noise images have drawn a lot of attention in recent years. There are many regularization methods to solve this problem and one of the most famous methods is the total variation model. In this paper, by adding a quadratic regularization on TGV regularization part, a new image restoration model is proposed based on second-order total generalized variation regularization. Then the split Bregman iteration algorithm was used to solve this new model. The experimental results show that the proposed model and algorithm can deal with Poisson image restoration problem well. What’s more, the restoration model performance is significantly improved both in visual effect and objective evaluation indexes.

Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations

This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ℓ1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition.