Split Bregman Approach Research Articles

Hypoxia-informed RBE-weighted beam orientation optimization for intensity modulated proton therapy.

Variable relative biological effectiveness (RBE) models in treatment planning have been proposed to optimize the therapeutic ratio of proton therapy. It has been reported that proton RBE decreases with increasing tumor oxygen level, offering an opportunity to address hypoxia-related radioresistance with RBE-weighted optimization. Here, we obtain a voxel-level estimation of partial oxygen pressure to weigh RBE values in a single biologically informed beam orientation optimization (BOO) algorithm. Three glioblastoma patients with [18 F]-fluoromisonidazole (FMISO)-PET/CT images were selected from the institutional database. Oxygen values were derived from tracer uptake using a nonlinear least squares curve fitting. McNamara RBE, calculated from proton dose, was then weighed using oxygen enhancement ratios (OER) for each voxel and incorporated into the dose fidelity term of the BOO algorithm. The nonlinear optimization problem was solved using a split-Bregman approach, with FISTA as the solver. The proposed hypoxia informed RBE-weighted method (HypRBE) was compared to dose fidelity terms using the constant RBE of 1.1 (cRBE) and the normoxic McNamara RBE model (RegRBE). Tumor homogeneity index (HI), maximum biological dose (Dmax), and D95%, as well as OAR therapeutic index (TI=gEUDCTV /gEUDOAR ) were evaluated along with worst-case statistics after normalization to normal tissue isotoxicity. Compared to [cRBE, RegRBE], HypRBE increased tumor HI, Dmax, and D95% across all plans by on average [31.3%, 31.8%], [48.6%, 27.1%], and [50.4%, 23.8%], respectively. In the worst-case scenario, the parameters increase on average by [12.5%, 14.7%], [7.3%,-8.9%], and [22.3%, 2.1%]. Despite increased OAR Dmean and Dmax by [8.0%, 3.0%] and [13.1%, -0.1%], HypRBE increased average TI by [22.0%, 21.1%]. Worst-case OAR Dmean, Dmax, and TI worsened by [17.9%, 4.3%], [24.5%, -1.2%], and [9.6%, 10.5%], but in the best cases, HypRBE escalates tumor coverage significantly without compromising OAR dose, increasing the therapeutic ratio. We have developed an optimization algorithm whose dose fidelity term accounts for hypoxia-informed RBE values. We have shown that HypRBE selects bE:\Alok\aaeams better suited to deliver high physical dose to low RBE, hypoxic tumor regions while sparing the radiosensitive normal tissue.

Hypoxia Informed RBE-Weighted Beam Orientation Optimization for Intensity Modulated Proton Therapy Using [18F]-FMISO-PET Estimation of pO2

Variable relative biological effectiveness (RBE) models have previously informed proton therapy dose optimization algorithms, but few models have incorporated hypoxia's increase on radioresistance. Here, we obtain voxel-based estimation of partial oxygen pressure to weigh RBE values in a single biologically informed beam orientation optimization (BOO) algorithm. Four brain cancer patients with [18F]-FMISO-PET/CT images were selected from an HCP database. Oxygen values were derived from tracer uptake using a non-linear least squares curve fitting. RBE dose was then weighted using oxygen enhancement ratios (OER) for each structure and substituted into the dose fidelity term of our BOO algorithm. The nonlinear optimization problem was solved using a split-Bregman approach, with FISTA as the solver. This method (HypRBE) was compared dose fidelity terms using the Rorvik RBE model (RegRBE), without OER. Tumor homogeneity index (HI), Dmax, and D95% were evaluated along with worst-case statistics after normalization to normal tissue isotoxicity. Compared to RegRBE, HypRBE increased tumor [HI, Dmax, D95%] on average by [0.5%, 2.0%, 2.5%] and improved worst-case tumor [HI, Dmax, D95%] by [5.3%, 16.2%, 9.6%]. HypRBE shows an increase in therapeutic ratio, and is notably robust against uncertainty scenarios. We have developed an optimization algorithm whose dose fidelity term is weighted by hypoxia informed RBE values. We have shown that HypRBE selects beams that are better suited to protect low RBE, well-oxygenated normal tissue while maintaining high dose to high RBE, hypoxic tumor cells.

Efficient non-blind deconvolution method for large scale blurred image with hybrid regularizations

We propose to combine a variety of regularization terms and design a non-blind image deconvolution algorithmic framework which is based on the split-Bregman approach. With the proposed algorithm, the original problem can be decomposed into simple sub-problems and solved efficiently by variable splitting and penalty technology. Furthermore, we also propose an acceleration scheme for restoring large scale blurred image which is based on image segmentation and parallel computing of GPU and multi-core CPU. Experimental results show that our approach can achieve restored image of high quality which is comparable with some state of the art methods, and the efficiency of the algorithm can be significantly enhanced with the proposed acceleration scheme for restoring large scale blurred image.

Split Bregman Approach to Linear Prediction Based Dereverberation With Enforced Speech Sparsity

The recordings of speech in enclosures are corrupted by reverberation caused by multipath wave propagation from the speaker to the distant microphones. In this letter, we address the problem of reducing the late part of room reverberation. The presented blind dereverberation method consists in multichannel linear prediction (MCLP) and enforces sparsity of the dereverberated speech by adopting the split Bregman approach. The proposed algorithm alternately solves two optimization problems, where the former cost function is derived by assuming that speech is modelled using a sparse prior distribution, while the latter optimization emphasizes speech sparsity by an additional incorporation of a weighted $\ell _1$ -norm of the output signal to the standard linear prediction based cost function. The results of experiments performed using simulated and measured room impulse responses for various reverberation time values indicate superior performance of the proposed sparse split Bregman (SSB) method over state-of-the-art non-sparse and sparse MCLP-based dereverberation methods in terms of standard evaluation measures and as pre-processsing to the automatic speech recognition.

Low-dose dynamic myocardial perfusion CT image reconstruction using pre-contrast normal-dose CT scan induced structure tensor total variation regularization

Dynamic myocardial perfusion CT (DMP-CT) imaging provides quantitative functional information for diagnosis and risk stratification of coronary artery disease by calculating myocardial perfusion hemodynamic parameter (MPHP) maps. However, the level of radiation delivered by dynamic sequential scan protocol can be potentially high. The purpose of this work is to develop a pre-contrast normal-dose scan induced structure tensor total variation regularization based on the penalized weighted least-squares (PWLS) criteria to improve the image quality of DMP-CT with a low-mAs CT acquisition. For simplicity, the present approach was termed as ‘PWLS-ndiSTV’. Specifically, the ndiSTV regularization takes into account the spatial-temporal structure information of DMP-CT data and further exploits the higher order derivatives of the objective images to enhance denoising performance. Subsequently, an effective optimization algorithm based on the split-Bregman approach was adopted to minimize the associative objective function. Evaluations with modified dynamic XCAT phantom and preclinical porcine datasets have demonstrated that the proposed PWLS-ndiSTV approach can achieve promising gains over other existing approaches in terms of noise-induced artifacts mitigation, edge details preservation, and accurate MPHP maps calculation.

Validation of a quantitative susceptibility mapping acquisition and reconstruction pipeline using a new iron sucrose based MR susceptibility phantom

PurposeQuantitative susceptibility mapping is a new technique and its processing pipeline has to be validated before clinical practice. We described an easy to build magnetic resonance (MR) susceptibility phantom based on iron sucrose. Materials and methodsIn a plastic container, Eppendorf tubes containing increasing iron sucrose concentration ranging from 0 to 60μg Fe/mL were inserted in an agarose gel. To estimate susceptibility, multiple coronal gradient echo acquisitions were performed with varying angle of the phantom relative to the B0 field, ranging from 30 to 90°. Quantitative susceptibility maps were reconstructed using the l1 and l2 norm of total variation using Split Bregman approach. Iron concentration was finally estimated from the susceptibility in the tubes. ResultsIn l1 norm susceptibility and estimated iron concentration were not different from the real values while l2 norm underestimated the susceptibility. A correlation was found between the angle of the phantom and the difference between real and estimated iron concentrations. The results highlight the importance of this validation by emphasizing the effects of various reconstruction parameters as well as acquisition conditions. Using optimal parameters, the quantitative susceptibility mapping provides a very good estimation of the iron concentrations in the phantom.

Destripe Hyperspectral Images with Spectral-spatial Adaptive Unidirectional Variation and Sparse Representation

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable l1-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.

Revisiting the redistancing problem using the Hopf–Lax formula

This article presents a fast new numerical method for redistancing objective functions based on the Hopf–Lax formula [1]. The algorithm suggested here is a special case of the previous work in [2] and an extension that applies the Hopf–Lax formula for computing the signed distance to the front. We propose the split Bregman approach to solve the minimization problem as a solution of the eikonal equation obtained from Hopf–Lax formula. Our redistancing procedure is expected to be generalized and widely applied to many fields such as computational fluid dynamics, the minimal surface problem, and elsewhere.

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.

Hyperspectral Image Denoising Using Spatio-Spectral Total Variation

This letter introduces a hyperspectral denoising algorithm based on spatio-spectral total variation. The denoising problem has been formulated as a mixed noise reduction problem. A general noise model has been considered which accounts for not only Gaussian noise but also sparse noise. The inherent structure of hyperspectral images has been exploited by utilizing 2-D total variation along the spatial dimension and 1-D total variation along the spectral dimension. The denoising problem has been formulated as an optimization problem whose solution has been derived using the split-Bregman approach. Experimental results demonstrate that the proposed algorithm is able to reduce a significant amount of noise from real noisy hyperspectral images. The proposed algorithm has been compared with existing state-of-the-art approaches. The quantitative and qualitative results demonstrate the superiority of the proposed algorithm in terms of peak signal-to-noise ratio, structural similarity, and the visual quality.

Energy efficient EEG sensing and transmission for wireless body area networks: A blind compressed sensing approach

The problem of recovering multi-channel EEG signals from their randomly under-sampled measurements is addressed. The objective is to reduce the energy consumed by sensing, processing and transmission in an EEG wireless body area network. Our work is based on the Blind Compressed Sensing (BCS) framework, however instead of exploiting only the sparsity of the multi-channel ensemble in a learned basis, we also make use of the ensembles’ approximate rank deficiency. Our proposed formulation requires solving new optimization problems. To solve these problems, we derive algorithms based on the Split Bregman approach. The resulting recovery results are considerably better than those of previous techniques, in terms of the quantitative and qualitative evaluations.

Investigation of different sparsity transforms for the PICCS algorithm in small-animal respiratory gated CT.

Respiratory gating helps to overcome the problem of breathing motion in cardiothoracic small-animal imaging by acquiring multiple images for each projection angle and then assigning projections to different phases. When this approach is used with a dose similar to that of a static acquisition, a low number of noisy projections are available for the reconstruction of each respiratory phase, thus leading to streak artifacts in the reconstructed images. This problem can be alleviated using a prior image constrained compressed sensing (PICCS) algorithm, which enables accurate reconstruction of highly undersampled data when a prior image is available. We compared variants of the PICCS algorithm with different transforms in the prior penalty function: gradient, unitary, and wavelet transform. In all cases the problem was solved using the Split Bregman approach, which is efficient for convex constrained optimization. The algorithms were evaluated using simulations generated from data previously acquired on a micro-CT scanner following a high-dose protocol (four times the dose of a standard static protocol). The resulting data were used to simulate scenarios with different dose levels and numbers of projections. All compressed sensing methods performed very similarly in terms of noise, spatiotemporal resolution, and streak reduction, and filtered back-projection was greatly improved. Nevertheless, the wavelet domain was found to be less prone to patchy cartoon-like artifacts than the commonly used gradient domain.

A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors

We present a scalable solver for approximating the maximum a posteriori (MAP) point of Bayesian inverse problems with Besov priors based on wavelet expansions with random coefficients. It is a subspace trust region interior reflective Newton conjugate gradient method for bound constrained optimization problems. The method combines the rapid locally-quadratic convergence rate properties of Newton's method, the effectiveness of trust region globalization for treating ill-conditioned problems, and the Eisenstat--Walker idea of preventing oversolving. We demonstrate the scalability of the proposed method on two inverse problems: a deconvolution problem and a coefficient inverse problem governed by elliptic partial differential equations. The numerical results show that the number of Newton iterations is independent of the number of wavelet coefficients $n$ and the computation time scales linearly in $n$. It will be numerically shown, under our implementations, that the proposed solver is two times faster than the split Bregman approach, and it is an order of magnitude less expensive than the interior path following primal-dual method. Our results also confirm the fact that the Besov $\mathbb{B}_{11}^1$ prior is sparsity promoting, discretization-invariant, and edge-preserving for both imaging and inverse problems governed by partial differential equations.

Weighted Elastic Net Penalized Mean-Variance Portfolio Design and Computation

It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the mean-variance objective function with a weighted elastic net penalty. We show that the use of this penalty can be motivated by a robust reformulation of the mean-variance criterion that directly accounts for parameter uncertainty. With this interpretation of the weighted elastic net penalty we derive data-driven techniques for calibrating the weighting parameters based on the level of uncertainty in the parameter estimates. We test our proposed technique on U.S. stock return data, and our results show that the calibrated weighted elastic net penalized portfolio outperforms both the unpenalized portfolio and the uniformly weighted elastic net penalized portfolio. This paper also introduces a novel adaptive support split-Bregman approach which leverages the sparse nature of $\e...

Exploiting Sparsity and Rank Deficiency for MR Image Reconstruction From Multiple Partial K-Space Scans

In magnetic resonance imaging, it is a common to acquire multiple scans of the K-space so that the effects of noise and motion artifacts can be reduced by averaging the K-space scans. However, sampling the full K-space is time consuming; to reduce the scan time, compressed sensing (CS)-based reconstruction algorithms are employed to recover images from partially sampled K-space scans. A recent study showed that the recovery can also be achieved by exploiting the rank deficiency of the underlying images. In this paper, we will show how the reconstruction can be further improved by combining CS techniques with low-rank recovery methods. Our proposed formulation leads to a least-square minimization problem that is regularized by an $l_{1}$ -norm and a nuclear norm. There is no efficient and accurate algorithm to solve this problem; therefore, we derive an algorithm to solve the said problem based on the Split Bregman approach. The results show that our proposed technique reduces the reconstruction error by about 40%.

Iterative CT Reconstruction Using Shearlet-Based Regularization

Total variation (TV) methods have been proposed to improve the image quality in count-reduced images, by reducing the variation between neighboring pixels. Although very easy to implement and fast to compute, TV-based methods may lead to a loss of texture information when applied to images with complex textures, such as high-resolution abdominal CT images. Here, we investigate the use of another regularization approach in the context of medical images based on multiresolution transformations. One such transformation is the shearlet transform, which is optimally sparse for images that are C2 except for discontinuities along C2 curves, and has better directional sensitivity than most other, related, wavelet transform approaches. We propose to solve the convex problem using the split-Bregman (augmented Lagrangian) approach. One of the primary advantages of the split-Bregman approach, is that the shearlet transform can easily be incorporated into the sparse-view CT reconstruction. The required sparsity prior is the l1 norm of the shearlet coefficients. Results are shown for this method in comparison to the same framework with TV as the regularization term on simulated data. The noise-resolution performance is investigated at different contrast levels. At equal image noise, TV-based regularization outperforms shearlet-based regularization. However, when image texture is analyzed on measured mouse data, shearlets outperform TV, which suffers from staircasing effects. Our results show that there are benefits in using shearlets in CT imaging: texture is reconstructed more accurately compared to when TV is used, without biasing the image towards a piecewise constant image model. However, due to the larger support of the basis functions, our results suggest that uncareful usage of shearlets may lead to wavy artifacts, which can be equally unwanted as staircasing effects.

A dual split Bregman method for fast $\ell ^1$ minimization

In this paper we propose a new algorithm for fast l1 minimization as frequently arising in compressed sensing. Our method is based on a split Bregman algorithm applied to the dual of the problem of minimizing ∥u∥1 + 1 2α ∥u∥2 such that u solves the under determined linear system Au = f , which was recently investigated in the context of linearized Bregman methods. Furthermore, we provide a convergence analysis for split Bregman methods in general and show with our compressed sensing example that a split Bregman approach to the primal energy can lead to a different type of convergence than split Bregman applied to the dual, thus making the analysis of different ways to minimize the same energy interesting for a wide variety of optimization problems.