Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

SIMRES-TV: NOISE AND RESIDUAL SIMILARITY FOR PARAMETER ESTIMATION IN TOTAL VARIATION

Image restoration with regularization models is very popular in the image processing literature. Total variation (TV) is one of the important edge preserving regularization models used, however, to obtain optimal restoration results the regularization parameter needs to be set appropriately. We propose here a new parameter estimation approach for total variation based image restoration. By utilizing known noise levels we compute the regularization parameter by reducing the similarity between residual and noise variances. We use the split Bregman algorithm for the total variation along with this automatic parameter estimation step to obtain a very fast restoration scheme. Experimental results indicate the proposed parameter estimation obtained better denoised images and videos in terms of PSNR and SSIM measures and the computational overload is less compared with other approaches.

An algorithm combining coordinate descent and split Bregman iterative for fractional image denoising model

The split Bregman algorithm and the coordinate descent method are efficient tools for solving optimization problems, which have been proven to be effective for the total variation model. We propose an algorithm for fractional total variation model in this paper, and employ the coordinate descent method to decompose the fractional-order minimization problem into scalar sub-problems, then solve the sub-problem by using split Bregman algorithm. Numerical results are presented in the end to demonstrate the superiority of the proposed algorithm.

Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this paper to achieve real-time imaging with an airborne radar. Firstly, under the regularization framework, the problem of azimuth resolution improvement can be converted into an L 1 regularization problem. Then, the L 1 regularization problem can be solved with the proposed FSBA. By utilizing the low displacement rank features of Toeplitz matrix, the proposed FSBA is able to realize fast matrix inversion by using a Gohberg–Semencul (GS) representation. Through simulated and real data processing experiments, we prove that the proposed FSBA significantly improves the resolution, compared with the Wiener filtering (WF), truncated singular value decomposition (TSVD), Tikhonov regularization (REGU), Richardson–Lucy (RL), iterative adaptive approach (IAA) algorithms. The computational advantage of FSBA increases with the increase of echo dimension. Its computational efficiency is 51 times and 77 times of the traditional SBA, respectively, for echoes with dimensions of 218 × 400 and 400 × 400 , optimizing both the image quality and computing time. In addition, for a specific hardware platform, the proposed FSBA can process echo of greater dimensions than traditional SBA. Furthermore, the proposed FSBA causes little performance degradation, when compared with the traditional SBA.

Split-Bregman Algorithm with Attenuation Correction for L-Shell Polychromatic X-ray Fluorescence Computed Tomography

L-shell X-ray fluorescence computed tomography based on polychromatic X-rays is a promising imaging technique for early cancer diagnosis. However, the presence of self-absorption and the long scanning time limit its usage in clinic. In this work, a reconstruction method based on split-Bregman algorithm which used sparseview projection data was proposed. Furthermore, the attenuation effect was also considered in the algorithm. In the attenuation correction, factors including the X-ray energy and the platinum concentration were taken into account. Then weighted factors calculated in the procedure of attenuation correction were added into the contribution function of pixels in the split-Bregman based reconstruction method. In the end, the feasibility of this method was tested using a cylindrical phantom with 8 mm in diameter by the Monte Carlo simulation. The phantom contained four inserts, all of which were 1.5 millimeter in diameter and filled with 0.10%, 0.20%, 0.40% and 0.80% platinum solutions, respectively. The results show that both the contrast-to-noise ratios and lowest detectable sensitivities are improved for the proposed method, comparing to the conventional MLEM. The contrast-to-noise ratios of images reconstructed by our method with 45 projections are already better than that reconstructed by MLEM with 60 projections. When using 60 projections in our method and comparing to 60 projections in the MLEM with correction, the contrast-to-noise ratio of the insert filled with 0.10% platinum solutions increased from 6.49 to 36.90, indicating its high efficiency and robustness.

A Shearlets-Based Method for Rain Removal from Single Images

This work focuses on the problem of rain removal from a single image. The directional multilevel system, Shearlets, is used to describe the intrinsic directional and structure sparse priors of rain streaks and the background layer. In this paper, a Shearlets-based convex rain removal model is proposed, which involves three sparse regularizers: including the sparse regularizer of rain streaks and two sparse regularizers of the Shearlets transform of background layer in the rain drops’ direction and the Shearlets transform of rain streaks in the perpendicular direction. The split Bregman algorithm is utilized to solve the proposed convex optimization model, which ensures the global optimal solution. Comparison tests with three state-of-the-art methods are implemented on synthetic and real rainy images, which suggests that the proposed method is efficient both in rain removal and details preservation of the background layer.