H-FISTA: a hierarchical algorithm for phase retrieval with application to pulsar dynamic spectra

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.

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.

Complementary with electroencephalograph (EEG), functional magnetic resonance imaging (fMRI), with high spatial resolution, is powerful at providing prior source locations based on actual brain physiology. It hereby can help improve the accuracy of EEG source localization. However, most of the current methods directly penalize the sources whose fMRI activation probability is low and estimate the sources activities at every time point. Thus, they do not account for the temporal interrelated and non-stationary features of electromagnetic brain signals, and some are too much dependent on the fMRI prior. Here, we propose a new fMRI informed EEG source localization method and is termed fMRI-informed spatio-temporal unifying tomography (FIST). It uses a mixed norm constraint defined in terms of time–frequency decomposition of the sources and combines it with fMRI prior. The Fast Iterative Shrinkage Thresholding Algorithm is employed to solve the optimization problem. Both simulated and real EEG data are applied to assess the performance of the proposed method. Compared with L2-norm constrained methods, FIST has the superiority brain source estimation both in the spatial and temporal domains. By virtue of the fMRI information as a prior, FIST has great improvement in spatial accuracy and computational efficiency, when comparing with the method which only uses mixed-norm constraint. In addition, FIST shows good ability to select the fMRI priors to get a better estimation without totally depending on the prior, when comparing with the method which also has fMRI prior information.

Quantitative differential phase-contrast (DPC) imaging is one of the commonly used methods for phase retrieval. However, quantitative DPC imaging requires several pairwise intensity measurements, which makes it difficult to monitor living cells in real-time. In this study, we present a single-shot quantitative DPC imaging method based on the combination of deep learning (DL) and color-encoded illumination. Our goal is to train a model that can generate an isotropic quantitative phase image (i.e., target) directly from a single-shot intensity measurement (i.e., input). The target phase image was reconstructed using a linear-gradient pupil with two-axis measurements, and the model input was the measured color intensities obtained from a radially asymmetric color-encoded illumination pattern. The DL-based model was trained, validated, and tested using thirteen different cell lines. The total number of training, validation, and testing images was 264 (10 cells), 10 (1 cell), and 40 (2 cells), respectively. Our results show that the DL-based phase images are visually similar to the ground-truth phase images and have a high structural similarity index (>0.98). Moreover, the phase difference between the ground-truth and DL-based phase images was smaller than 13%. Our study shows the feasibility of using DL to generate quantitative phase imaging from a single-shot intensity measurement.

Phase retrieval in DSSI for relatively large deformation

Typical quantitative refractive index (RI) imaging methods (e.g. optical diffraction tomography) use coherent illumination and interferometric detection to reconstruct 3D phase objects. We have developed a new technique to perform accurate ODT reconstructions using spatially incoherent illumination. This technique reconstructs the RI by minimizing the difference between simulated and interferometrically measured cross-correlation between the diffracted field and a reference image of the illumination, using the fast iterative shrinkage / thresholding algorithm (FISTA) framework. We numerically validate this technique by comparing results obtained with spatially incoherent illumination, to those obtained with coherent illumination, and obtain high-resolution reconstructions of similar quality.

Three-dimensional geostatistical inversion of synthetic tomographic pumping and heat-tracer tests in a nested-cell setup

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

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.

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