A novel Fourier-based deconvolution algorithm with improved efficiency and convergence

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.

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.

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.

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.

Discretized tensor-based model of total focusing method: A sparse regularization approach for enhanced ultrasonic phased array imaging

This paper denotes to obtain an accuracy blur kernel and a shape image. An efficient method that blind deconvolution for image deblurring based on edge enhancement and noise suppression is proposed. First, we exploited an edge detection method to extract the strong edge portion of blurred image. Then, the blurred image was divided into weak edge portion and strong edge portion. At this time, we apply a trilateral filter method to suppress the noise in the weak edge portion. Through mathematical operations for weak edge portion and strong edge portion, we can obtain the new blurred image which as the input of blur kernel estimation. At the phase of the kernel estimation, the problem can be solved via alternate between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> updating. In addition, we utilize improved fast iterative shrinkage thresholding algorithm method to solve the optimization problem. Finally, non-blind deconvolution was employed at the phase of image recovery. A comprehensive evaluation shows that our approach achieves state-of-the-art results for uniformly blurred images.

TEFISTA-Net: A learnable method for high-resolution range profile reconstruction with low-frequency ultra-wideband radar

3D Seismic Data Reconstruction based on Weighted Fast Iterative Shrinkage Thresholding algorithm

This paper investigates the damage detection of carbon fiber-reinforced polymer cables, which have the advantages of lightweight, high strength, and high corrosion resistance, for applications in engineering fields such as bridges and ropeways using electromagnetic tomography. To provide a solution to the issue of fast, high-quality imaging of carbon fiber-reinforced polymer cables in the presence of noise interference, a scheme for rotational excitation of the sensor array was designed, and an improved fast iterative shrinkage thresholding algorithm combined with total variation regularization was proposed. The imaging quality of carbon fiber-reinforced polymer cables with different damage was evaluated by numerical simulations and experiments. The results demonstrate that with each rotation of the sensor array, it increases the amount of independent measurement information. Furthermore, the proposed improved algorithm achieves a significantly reduced computation time compared to existing algorithms. Specifically, it is approximately 80% faster than Tikhonov’s algorithm and 72% faster than the Landweber algorithm. In addition, it demonstrates enhanced capability in capturing the intricate shape characteristics of damage while reducing the occurrence of artefacts. Finally, the electromagnetic tomography detection system was implemented, and the improved algorithm successfully achieved the damage detection of carbon fiber-reinforced polymer cables.

In preclinical radio-neuromodulation research, small animal experiments are pivotal for unraveling radiobiological mechanism, investigating prescription and planning techniques, and assessing treatment effects and toxicities. However, the target size inside a rat brain is typically in the order of sub-millimeters. The small target inside the visual cortex neural region in rat brain with a diameter of around 1mm was focused in this work to observe the physiological change of this region. Delivering uniform doses to the small target while sparing health tissues is challenging. Focused kV x-ray technique based on modern x-ray polycapillary focusing lens is a promising modality for small animal radio-neuromodulation. The current manual planning method could lead to sub-optimal plans, and the positioning uncertainties due to mechanical accuracy limitations, animal immobilization, and robotic arm motion are not considered. This work aims to design a robust inverse planning method to optimize the intensities of focused kV x-ray beams located in beam trajectories to irradiate small mm-sized targets in rat brains for radio-neuromodulation. Focused kV x-ray beams were generated through polycapillary x-ray focusing lenses on achieving small (≤0.3mm) focus perpendicular to the beam. The beam trajectories were manually designed in 3D space in scanning-while-rotating mode. Geant4 Monte Carlo (MC) simulation generated a dose calculation matrix for each focused kV x-ray beam located in beam trajectories. In the proposed robust inverse planning method, an objective function combining a voxel-wise stochastic programming approach and L1 norm regularization was established to overcome the positioning uncertainties and obtain a high-quality plan. The fast iterative shrinkage thresholding algorithm (FISTA) was utilized to solve the objective function and obtain the optimal intensities. Four cases were employed to validate the feasibility and effectiveness of the proposed method. The manual and non-robust inverse planning methods were also implemented for comparison. The proposed robust inverse planning method achieved superior dose homogeneity and higher robustness against positioning uncertainties. On average, the clinical target volume (CTV) homogeneity index (HI) of robust inverse plan improved to 13.3 from 22.9 in non-robust inverse plan and 53.8 in manual plan if positioning uncertainties were also present. The average bandwidth at D90 was reduced by 6.5Gy in the robust inverse plan, compared to 9.6Gy in non-robust inverse plan and 12.5Gy in manual plan. The average bandwidth at D80 was reduced by 3.4Gy in robust inverse plan, compared to 5.5Gy in non-robust inverse plan and 8.5Gy in manual plan. Moreover, the dose delivery time of manual plan was reduced by an average reduction of 54.7% with robust inverse plan and 29.0% with non-robust inverse plan. Compared to manual and non-robust inverse planning methods, the robust inverse planning method improved the dose homogeneity and delivery efficiency and was resistant to the uncertainties, which are crucial for radio-neuromodulation utilizing focused kV x-rays.

The proliferation of active radar sensors deployed in vehicles has increased the need for mitigating automotive radar-to-radar interference. While simple avoidance and mitigation methods are still effective today, the expected crowded spectrum allocations pose new challenges that likely require more sophisticated techniques. In particular, interference mitigation methods that can handle significant levels of radar signal corruption are required. To this end, we propose neurally augmented analytically learned fast iterative shrinkage thresholding algorithm (NA-ALFISTA), which is a neural network-based solution for reconstructing time-domain radar signals by leveraging sparsity in the range-Doppler map (RDM). The neural augmentation network is deployed as a single gated recurrent unit (GRU) cell that captures the radar signal statistics along the unfolded layers of fast-iterative shrinkage thresholding algorithm (FISTA)-based sparse recovery, which significantly boosts the convergence rate. It estimates the next layer’s parameters necessary in ALFISTA based on the previous layer’s output. The proposed method is compared to state-of-the-art detect-and-repair methods and source separation methods in simulated data and real-world measurements.

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.

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. Solving for the L and S components is anonsmooth composite convex minimization problem. While current techniques for this model are based on the classical iterative soft thresholding algorithm (ISTA), accelerated methods can be applied to obtain faster rate of convergence of the algorithm. This paper proposes two alternative methods for solving the L+S problem, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other based on the recent proximal optimized gradient method (POGM). Numerical results suggest faster convergence than the traditional ISTA, while preserving its computational simplicity.