Accelerated methods for low-rank plus sparse image reconstruction

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of under-sampled dynamic parallel magnetic resonance imaging (MRI) data. Solving for the low-rank and the sparse components involves non-smooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes. While current proximal gradient techniques for the L+S model involve the classical iterative soft thresholding algorithm (ISTA), this paper considers two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of the efficient implementations for both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.

Various deconvolution algorithms for acoustic source are developed to improve spatial resolution and suppress sidelobe of the conventional beamforming. To improve the computational efficiency and solution convergence of deconvolution, this paper proposes a Fourier-based improved fast iterative shrinkage thresholding algorithm. Simulations and experiments show that Fourier-based improved fast iterative shrinkage thresholding algorithm can achieve excellent acoustic identification performance, with high computational efficiency and good convergence. For Fourier-based improved fast iterative shrinkage thresholding algorithm, the larger the weight coefficient, the narrower the mainlobe width, and the better the convergence, but the spurious source also increases. The recommended weight coefficient for the array described herein is 3. In addition, like other Fourier-based deconvolution algorithms, Fourier-based improved fast iterative shrinkage thresholding algorithm using irregular focus grid can obtain better acoustic source identification performance than using the conventional regular focus grid.

Magnetotelluric (MT) sounding data are easily contaminated by various noise sources, especially noise with a long duration (even full-time noise), which makes it difficult to obtain accurate values when calculating the weight factors of the response function, resulting in distortion of the response results. Based on blind source separation theory, fast independent component analysis (FastICA) can separate this kind of noise. However, this method is challenged by the number of separated field sources and the unequal signal amplitude before and after processing. We have developed a novel signal noise separation method, improving the traditional FastICA, where a correlation coefficient is used to compute the number of field sources, and the fast iterative shrinkage threshold algorithm (FISTA) is used to adjust the signal amplitude problem before and after FastICA decomposition. Compared with common field source division methods and the traditional FastICA, the experimental results indicate that our method can separate and remove noise with a long duration, increase the signal-to-noise ratio of the data, and improve the MT response curves. Meanwhile, case studies of measured data illustrate that our method obtains a more robust magnetotelluric response than the conventional robust method and FastICA.

Accelerated parabolic Radon domain 2D adaptive multiple subtraction with fast iterative shrinkage thresholding algorithm and its application in parabolic Radon domain hybrid demultiple method

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

Compressive sensing magnetic resonance (MR) imaging is aimed at achieving high-quality MR image reconstruction by undersampling K-space data. It is crucial to explore prior information since compressive sensing MR imaging relies heavily on some prior assumptions, such as signal's sparse property. In this study, in order to explore the prior information fully, an improved MR image reconstruction model based on compressive sensing theory is proposed, named reference image MR imaging with adaptive tight frame. In the proposed model, an adaptive tight frame is involved to explore the sparse prior information adapt to MR images and the similarity prior information to the target image. Meanwhile, improved adaptive weighting parameters are used to trade off the sparsity between the regions with much similarity and that of little similarity. In addition, the smoothing-based fast iterative shrinkage-threshold algorithm is utilised to tackle the optimisation problem so as to speed up imaging. The experimental results demonstrate that the proposed MR image reconstruction method outperforms some state-of-the-art methods in terms of quantitative results.

Magnetic resonance imaging systems usually feature linear and shift-invariant (stationary) transform characteristics. The point spread function or equivalently the modulation transfer function may thus be used for an objective quality assessment of imaging modalities. The recently introduced theory of compressed sensing, however, incorporates nonlinear and nonstationary reconstruction algorithms into the magnetic resonance imaging process which prohibits the usage of the classical point spread function and therefore the according evaluation. In this work, a local point spread function concept was applied to assess the quality of magnetic resonance images which were reconstructed by an iterative soft thresholding algorithm for compressed sensing. The width of the main lobe of the local point spread function was used to perform studies on the spatial and temporal resolution properties of both numerical phantom and in vivo images. The impact of k-space sampling patterns as well as additional sparsifying transforms on the local spatial image resolution was investigated. In addition, the local temporal resolution of image series, which were reconstructed by exploiting spatiotemporal sparsity, was determined. Finally, the dependency of the local resolution on the thresholding parameter of the algorithm was examined. The sampling patterns as well as the additional sparsifying transform showed a distinct impact on the local image resolution of the phantom image. The reconstructions, which were using x-f-space as a sparse transform domain showed slight temporal blurring for dynamic parts of the imaged object. The local image resolution had a dependence on the thresholding parameter, which allowed for optimizing the reconstruction. Local point spread functions enable the evaluation of the local spatial and temporal resolution of images reconstructed with the nonlinear and nonstationary iterative soft thresholding algorithm. By determining the influence of thresholding parameter and sampling pattern chosen on this model-based reconstruction, the method allows selecting appropriate acquisition parameters and thus improving the results.

Orthogonal transformations, proper decomposition, and the Moore–Penrose inverse are traditional methods of obtaining the output layer weights for an extreme learning machine autoencoder. However, an increase in the number of hidden neurons causes higher convergence times and computational complexity, whereas the generalization capability is low when the number of neurons is small. One way to address this issue is to use the fast iterative shrinkage-thresholding algorithm (FISTA) to minimize the output weights of the extreme learning machine. In this work, we aim to improve the convergence speed of FISTA by using two fast algorithms of the shrinkage-thresholding class, called greedy FISTA (G-FISTA) and linearly convergent FISTA (LC-FISTA). Our method is an exciting proposal for decision-making involving the resolution of many application problems, especially those requiring longer computational times. In our experiments, we adopt six public datasets that are frequently used in machine learning: MNIST, NORB, CIFAR10, UMist, Caltech256, and Stanford Cars. We apply several metrics to evaluate the performance of our method, and the object of comparison is the FISTA algorithm due to its popularity for neural network training. The experimental results show that G-FISTA and LC-FISTA achieve higher convergence speeds in the autoencoder training process; for example, in the Stanford Cars dataset, G-FISTA and LC-FISTA are faster than FISTA by 48.42% and 47.32%, respectively. Overall, all three algorithms maintain good values of the performance metrics on all databases.

Spaceborne airborne bistatic linear array synthetic aperture radar (SA-BiLASAR) is a novel type of bistatic SAR (BiSAR) with multi-view three-dimensional (3-D) imaging capabilities. However, due to the separation of transceiver platforms and the structure of linear array antenna, the form of its motion errors is variable. Hence the estimation and compensation of its motion errors are more difficult than traditional SAR system. In this paper, an autofocus method is proposed for SA-BiLASAR 3-D sparse imaging based on maximum sharpness estimation (MSE). Firstly, the sparse imaging model of SA-BiLASAR and the spatial-variant characteristic of its motion errors are discussed. Secondly, combined with the MSE principle, the reconstruct procedure of SA-BiLASAR is presented via fast iterative shrinkage thresholding algorithm (FISTA). Lastly, the complex motion errors of SA-BiLASAR are estimated and compensated by the proposed method. Simulation results demonstrate the effectiveness of the sparse autofocus approach in the case of the different types of motion errors.

The iterative soft thresholding algorithm (ISTA) is one of the most popular optimization algorithms for solving the regularized least squares problem, and its linear convergence has been investigated under the assumption of finite basis injectivity property or strict sparsity pattern. In this paper, we consider the regularized least squares problem in finite- or infinite-dimensional Hilbert space, introduce a weaker notion of orthogonal sparsity pattern (OSP) and establish the Q-linear convergence of ISTA under the assumption of OSP. Examples are provided to illustrate the cases where the linear convergence of ISTA can be established only by our result, but cannot be ensured by any existing result in the literature.

The fast iterative shrinkage-thresholding algorithm (FISTA) is a well-known first order method used to minimize <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> regularized problems. However, it is also a non-monotone algorithm that can exhibit a sudden and gradual oscillatory behavior during the convergence. One of the parameters that directly affects the convergence of the FISTA method, whose optimal value is typically unknown, is the step-size (SS) that is linked to the Lipschitz constant. Depending on a suitable selection of the SS either manual or automatic, and the SS evolution throughout iterations, e.g. constant, decreasing, or increasing sequence, the practical performance can differ in orders of magnitude with or without stability issues (oscillations or, in the worst case, divergence). In this paper, we propose an algorithm, which has two variants, to address the stability issues in case of ill-chosen parameters for a given SS policy (either manual or adaptive). The proposed method structurally consists of an instability prediction rule based on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{\infty}$</tex> norm of the gradient, and a correction for it, which can interpreted as an under-relaxation technique.

&lt;sec&gt;An algorithm of reconstructing phaseless radiation source based on singular value decomposition (SVD) regularization and fast iterative shrinkage-thresholding algorithm (FISTA) is proposed in this work, aiming at efficiently identifying electromagnetic interference (EMI) sources in integrated circuits (ICs). The method acquires electromagnetic field data through near-field scanning and reconstructs an equivalent dipole array on the surface of the radiation source by using the source reconstruction method (SRM). In the reconstruction process, the SVD regularization term enhances the algorithm's stability and noise resistance, while the FISTA accelerates the convergence speed.&lt;/sec&gt;&lt;sec&gt;In order to validate the effectiveness of the proposed method, dipole array reconstruction is first performed using near-field data at a height of 5 mm for a patch antenna simulation model, followed by analyzing the magnetic field data at a 10 mm validation plane. At the 35th iteration, the total relative error of the reconstruction is 1.21%. The influence of the regularization parameter &lt;i&gt;α&lt;/i&gt; on the result is then investigated, and it is found that when &lt;i&gt;α&lt;/i&gt; = 0.05 the error is minimized. The method is also tested under different Gaussian white noise conditions, and the relative error is kept below 5%, which demonstrates strong robustness.&lt;/sec&gt;&lt;sec&gt;Finally, the experiments on chips are conducted to verify the method. The proposed method converges stably within 35 iterations, with a relative error of 2.3% in the reconstruction results. The proposed method reduces the total iteration time to 61.7% of the single-layer phaseless interpolation algorithm, while achieving a 52% lower relative error than the double-layer phasless iteration algorithm. The experimental results show that the proposed method can reconstruct phaseless radiation source efficiently and accurately, and has good noise robustness, which is suitable for EMI analysis in ICs.&lt;/sec&gt;

The construction of brain functional network based on resting-state functional magnetic resonance imaging (fMRI) is an effective method to reveal the mechanism of human brain operation, but the common brain functional network generally contains a lot of noise, which leads to wrong analysis results. In this paper, the least absolute shrinkage and selection operator (LASSO) model in compressed sensing is used to reconstruct the brain functional network. This model uses the sparsity of L1-norm penalty term to avoid over fitting problem. Then, it is solved by the fast iterative shrinkage-thresholding algorithm (FISTA), which updates the variables through a shrinkage threshold operation in each iteration to converge to the global optimal solution. The experimental results show that compared with other methods, this method can improve the accuracy of noise reduction and reconstruction of brain functional network to more than 98%, effectively suppress the noise, and help to better explore the function of human brain in noisy environment.

Bioluminescence Tomography (BLT) is one kind of optical molecular imaging modality, whose principle is to estimate the three-dimensional spatial distribution of bioluminescent sources by using the optical information obtained from the surface of the imaging object. Due to the scattering effect of light and the limitation of detected surface photons, BLT has become an ill-posed problem, and the existing methods make it difficult to obtain satisfactory reconstruction results. To solve the sparse reconstruction problem of BLT, a support-driven adaptive Bayesian reweighted momentum iterative acceleration algorithm (SABR-MIA) is proposed to transform the optimization problem into a series of iteratively weighted subproblems. According to the "non-zero support" of the current iterative solution, the weights are adjusted dynamically, and the regularization weights of each component are updated based on Bayesian prior, thus effectively improving the reconstruction accuracy. Secondly, in the iterative process, to accelerate the convergence and enhance computational efficiency, this paper adopts the momentum iterative acceleration strategy (MIA). Specifically, based on the fast iterative shrinkage threshold algorithm (FISTA), adaptive threshold shrinkage is introduced, and the Nesterov acceleration strategy is combined to optimize gradient update. Simulation results confirm the method's effectiveness in reconstruction quality and accuracy.Clinical Relevance- The SABR-MIA method can significantly improve the quality of sparse reconstruction of BLT, which is conducive to further application in clinical studies such as cell tracking and tumor monitoring.

In this paper, we present a fast iterative magnetic resonance imaging (MRI) reconstruction algorithm taking advantage of the prevailing GPGPU programming paradigm. In clinical environment, MRI reconstruction is usually performed via fast Fourier transform (FFT). However, imaging artifacts (i.e. signal loss) resulting from susceptibility-induced magnetic field inhomogeneities degrade the quality of reconstructed images. These artifacts must be addressed using accurate modeling of the physics of the system coupled with iterative reconstruction. We have developed a reconstruction algorithm with improved image quality at the expense of computation time and hence an implementation on GPUs achieving significant speedup. In this work, we extend our previous work on GPU implementation by adding several new features. First, we enable Sensitivity Encoding for Fast MRI (SENSE) reconstruction (from data acquired using a multi-receiver coil array) which can reduce the acquisition time. Besides, we have implemented a GPU-based total variation regularization in our SENSE reconstruction framework. In this paper, we describe the different optimizations employed from levels of algorithm, program code structures, and specific architecture performance tuning, featuring both our MRI reconstruction algorithm and GPU hardware specifics. Results show that the current GPU implementation produces accurate image estimates while significantly accelerating the reconstruction.