Fast Iterative Shrinkage Thresholding Research Articles

CTV-Net: Complex-Valued TV-Driven Network With Nested Topology for 3-D SAR Imaging.

The regularization-based approaches offer promise in improving synthetic aperture radar (SAR) imaging quality while reducing system complexity. However, the widely applied l1 regularization model is hindered by their hypothesis of inherent sparsity, causing unreal estimations of surface-like targets. Inspired by the edge-preserving property of total variation (TV), we propose a new complex-valued TV (CTV)-driven interpretable neural network with nested topology, i.e., CTV-Net, for 3-D SAR imaging. In our scheme, based on the 2-D holography imaging operator, the CTV-driven optimization model is constructed to pursue precise estimations in weakly sparse scenarios. Subsequently, a nested algorithmic framework, i.e., complex-valued TV-driven fast iterative shrinkage thresholding (CTV-FIST), is derived from the theory of proximal gradient descent (PGD) and FIST algorithm, theoretically supporting the design of CTV-Net. In CTV-Net, the trainable weights are layer-varied and functionally relevant to the hyperparameters of CTV-FIST, which aims to constrain the algorithmic parameters to update in a well-conditioned tendency. All weights are learned by end-to-end training based on a two-term cost function, which bounds the measurement fidelity and TV norm simultaneously. Under the guidance of the SAR signal model, a reasonably sized training set is generated, by randomly selecting reference images from the MNIST set and consequently synthesizing complex-valued label signals. Finally, the methodology is validated, numerically and visually, by extensive SAR simulations and real-measured experiments, and the results demonstrate the viability and efficiency of the proposed CTV-Net in the cases of recovering 3-D SAR images from incomplete echoes.

Robust treatment planning for small animal radio-neuromodulation using focused kV x-ray beams.

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.

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

In low-frequency ultra-wideband (LFW) radar, the reconstruction of high-resolution range profile (HRRP) is an important task. The state-of-the-art compressive sensing (CS) method for HRRP reconstruction based on geometrical theory of diffraction (GTD) requires manual algorithm parameter tuning and is computationally expensive. In this paper, we propose a deep learning-based CS method for LFW radar HRRP reconstruction. We design a neural network architecture, i.e., target enhancement-based FISTA-Net (TEFISTA-Net), by unrolling the fast iterative shrinkage thresholding algorithm (FISTA). A new loss function based on the target-to-background ratio (TBR) is introduced for network training with the target enhancement capability in low signal-to-noise ratio (SNR) scenarios. The algorithm parameters in the traditional CS methods are substituted by network parameters learned from training data, getting rid of manual parameter tuning. In addition, simple convolution operations in our new method lead to lower computational complexity compared with existing methods. Experimental results based on diverse data show that the proposed method leads to higher computational efficiency with similar or better performance in comparison with existing state-of-the-art methods.

Automatic Modulation Recognition Based on a New Deep K-SVD Denoising Algorithm

Automatic modulation recognition has a wide range of applications in wireless communication. To solve the problem that the previous methods convert signal modulation recognition into image recognition, leading to increased time costs and information loss, an automatic modulation recognition approach consisting of the improved deep K-SVD denoising algorithm is suggested. First, the effectiveness of the model for random sine wave denoising is demonstrated by simulation. Second, the original I/Q signals are fed into the modified deep K-SVD model for denoising, skipping the complicated image processing steps. Finally, the noise-reduced signals are input into a multi-channel convolutional long short-term neural network to complete the modulation recognition. To solve the slow convergence problem of Iterative Shrinkage Thresholding Algorithms in sparse coding, the Fast Iterative Shrinkage Thresholding Algorithm is adopted to improve the computational efficiency and obtain a better denoising effect. The experiments show that the improved model has an average recognition accuracy of 91.26% at different SNRs from -2 dB to 18 dB, which is better than the state-of-the-art modulation recognition models.

HFIST-Net: High-throughput fast iterative shrinkage thresholding network for accelerating MR image reconstruction

Background and ObjectivesCompressed sensing (CS) is often used to accelerate magnetic resonance image (MRI) reconstruction from undersampled k-space data. A novelty deeply unfolded networks (DUNs) based method, designed by unfolding a traditional CS-MRI optimization algorithm into deep networks, can provide significantly faster reconstruction speeds than traditional CS-MRI methods while improving image quality. MethodsIn this paper, we propose a High-Throughput Fast Iterative Shrinkage Thresholding Network (HFIST-Net) for reconstructing MR images from sparse measurements by combining traditional model-based CS techniques and data-driven deep learning methods. Specifically, the conventional Fast Iterative Shrinkage Thresholding Algorithm (FISTA) method is expanded as a deep network. To break the bottleneck of information transmission, a multi-channel fusion mechanism is proposed to improve the efficiency of information transmission between adjacent network stages. Moreover, a simple yet efficient channel attention block, called Gaussian context transformer (GCT), is proposed to improve the characterization capabilities of deep Convolutional Neural Network (CNN,) which utilizes Gaussian functions that satisfy preset relationships to achieve context feature excitation. ResultsT1 and T2 brain MR images from the FastMRI dataset are used to validate the performance of the proposed HFIST-Net. The qualitative and quantitative results showed that our method is superior to those compared state-of-the-art unfolded deep learning networks. ConclusionsThe proposed HFIST-Net is capable of reconstructing more accurate MR image details from highly undersampled k-space data while maintaining fast computational speed.

An Acoustic Localization Sensor Based on MEMS Microphone Array for Partial Discharge.

Partial discharge (PD) localization is important for monitoring and maintaining high-voltage equipment, which can help to prevent accidents. In this work, an acoustic localization sensor based on microelectromechanical system (MEMS) microphone array is proposed, which can detect and locate the partial discharge through a beam-forming algorithm. The MEMS microphone array consists of eight commercial MEMS microphones (SPV08A0LR5H-1, Knowles Electronics, IL, USA) with an aperture size of about 0.1 m × 0.1 m, allowing for a small hardware size and low cost. In order to optimize the acoustic performance of the array, a random array topology is designed. The simulation analysis indicates that the designed random topology is superior to several commonly used topologies. In terms of the localization algorithm, a deconvolution method called Fourier-based fast iterative shrinkage thresholding algorithm (FFT-FISTA) is applied. Simulation and experiment results demonstrate that FFT-FISTA used in the proposed acoustic localization sensor has significant advantages over the conventional beam-forming algorithm on spatial resolution and sidelobe suppression. Experimental results also show that the average localization error of the proposed scheme is about 0.04 m, which can meet the demands of practical application.

A Graph-guided Hybrid Regularization Method For Bioluminescence Tomography

Background and objective: Bioluminescence tomography (BLT) is a powerful and sensitive imaging technique having great potential in preclinical application, such as tumor imaging, monitoring and therapy, etc. Regularization plays an important role in BLT reconstruction for considering the priori information to overcome the inherent ill-posedness of the inverse problem. Therefore, well-designed regularization term and sophisticated algorithm for solving the consequent optimization problem are key to improve the BLT quality.Methods: To balance the sparsity, smoothness and morphological characteristics of the bioluminescence targets, we constructed a novel Graph-Guided Hybrid Regularization (GGHR) method by combining graph-guided penalty term with L1 and L2 norm regularizer. To solve the corresponding minimization problem with hybrid penalties, the dual decomposition and Nesterov’s smoothing technique were adopted to decouple and transform the non-separable and non-smooth graph-guided penalty term into a differential smooth approximation form, which was solved by the fast iterative shrinkage thresholding algorithm.Results: The performance of the proposed GGHR method was verified and evaluated through a series of simulation, phantom and in vivo experiments. The comparison results demonstrated that the GGHR method outperformed current mainstream reconstruction algorithms in spatial localization, morphology recovery and in vivo practicality.Conclusions: The proposed GGHR method is a robust and practicality reconstruction algorithm for further highlighting the positive effect of hybrid regularization on BLT applications.

A Robust Sparse Imaging Algorithm Using Joint MIMO Array Manifold and Array Channel Outliers

The multiple-input multiple-output (MIMO) radar imaging technology has attracted many scholars due to its many inherent advantages, such as avoiding complex motion compensation and imaging a quickly maneuvering target, compared to inverse synthetic aperture radar (ISAR) imaging. Although some imaging algorithms, such as the 2D fast iterative shrinkage thresholding algorithm (2D-FISTA), can meet the demand for super-resolution, they are not directly suited to MIMO radar imaging, for which the MIMO manifold needs to be considered. In this paper, based on the above questions, we propose the MIMO radar imaging algorithm, utilizing the sparsity of the scattering map in space and the MIMO array manifold, even achieving a good performance in the presence of MIMO channel error. The sparse reconstruction algorithm is developed with the alternative direction method of multipliers (ADMM) with the help of 2D-FISTA and the lp-norm. Then, two algorithms are derived: one is the exact sparse recovery algorithm, and the other is the inexact sparse recovery algorithm. Although the exact sparse recovery algorithm can converge to a more accurate precision than the inexact algorithm, the latter can converge at a faster speed. Finally, the results on simulation data validated the effectiveness of the algorithm.

Some modified fast iterative shrinkage thresholding algorithms with a new adaptive non-monotone stepsize strategy for nonsmooth and convex minimization problems

Some modified fast iterative shrinkage thresholding algorithms with a new adaptive non-monotone stepsize strategy for nonsmooth and convex minimization problems

Modelling short-term variations of differential code bias aiding in extraction of ionospheric observables with sparse kernel learning

As short-term variations existing in differential code bias of receivers (RDCB) will decrease the accuracies of extracting ionospheric observables by carrier-to-code leveling (CCL) method, a modified carrier-to code leveling (MCCL) method had been proposed to estimate RDCB offsets epoch by epoch in retrieval of ionospheric information. However, MCCL method is hampered by efficiency and precision at higher sampling intervals. To address RDCB offsets in higher sampling rate domain, a kernel model in the form of radial basis function (RBF) was chosen to model RDCB offsets produced by MCCL using lower sampling rate data in this paper. Owing to ill-posed problem induced by setting to many kernels, L1 norm regulation was employed to promote the sparsity of the problem and Fast iterative shrinkage thresholding algorithm (FISTA) was adopted to find the sparse solution. Data sets of 350 IGS stations evenly distributed in high-solar and low-solar activity years were chosen to illustrate the general existences of RDCB offsets and their dependence on solar activity. To validate the reliability and efficiency of the proposed method, two stations of them were selected out to construct the spares kernel model. As shown in experimental results, kernel model is of good performance in training data with over 90% sparsity rate and all standard deviations of the errors between original and fitting data are around 0.4 ns. It is a striking finding in terms of efficiency that the proposed method and CCL are much more efficient than MCCL in extracting ionospheric observables by means of fixed equipment. For further validations, generalized triangular series function (GTSF) was constructed using ionospheric observables derived from precise point positioning (PPP), CCL, MCCL and the proposed method. With Center for Orbit Determination in Europe (CODE) Global Ionospheric Map (GIM) regarded as reference, compared with VTEC estimates derived from CCL, those derived from MCCL and the proposed method have improved accuracies ranging from 10% to 20%. Overall, these results indicate that the proposed method has a promising application in retrieval of ionospheric observables in terms of accuracy and efficiency.

CSI Feedback With Model-Driven Deep Learning of Massive MIMO Systems

In order to achieve reliable communication with a high data rate of massive multiple-input multiple-output (MIMO) systems in frequency division duplex (FDD) mode, the estimated channel state information (CSI) at the receiver needs to be fed back to the transmitter. However, the feedback overhead becomes exorbitant with the increasing number of antennas. In this letter, a two stages low rank (TSLR) CSI feedback scheme for millimeter wave (mmWave) massive MIMO systems is proposed to reduce the feedback overhead based on model-driven deep learning. Besides, we design a deep iterative neural network, named FISTA-Net, by unfolding the fast iterative shrinkage thresholding algorithm (FISTA) to achieve more efficient CSI feedback. Moreover, a shrinkage thresholding network (ST-Net) is designed in FISTA-Net based on the attention mechanism, which can choose the threshold adaptively. Simulation results show that the proposed TSLR CSI feedback scheme and FISTA-Net outperform the existing algorithms in various scenarios.

RFI Source Detection Based on Reweighted ℓ 1-Norm Minimization for Microwave Interferometric Radiometry

Radio frequency interference (RFI) seriously deteriorates the quality of the retrieval of geophysical parameters, e.g., Earth surface moisture and ocean salinity, measured in microwave interferometric radiometry (MIR). The accurate detection of RFI sources is crucial for locating these illegal sources and mitigating their impact. In this article, we propose a new method based on reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm minimization to detect RFI sources. First, we exploit the sparsity of RFI sources in the spatial domain and formulate the RFI detection as a problem of reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm minimization, by which the RFI signals can be well recovered and the background noises can be suppressed. Then, we present two algorithms, termed RL1 and NRL1, to achieve RFI source detection. The RL1 algorithm employs a fast iterative shrinkage thresholding (FIST) technique, and the NRL1 algorithm combines the FIST with a neighbor-reweighting strategy that helps to further enhance the RFI target regions. Finally, simulations and experiments using Soil Moisture and Ocean Salinity (SMOS) satellite data demonstrate the superiority of the proposed method on the RFI-signal-to-background ratio (RSBR) in recovered images and the detection performance of RFI sources, compared with the existing RFI processing methods in MIR.

Evaluation of Optimization Algorithms and Noise Robustness of Sparsity-Promoting Dynamic Mode Decomposition

In the present study, we organize the existing sparsity-promoting dynamic mode decomposition (DMDsp) in terms of noise robustness, propose faster optimization algorithm for DMDsp, and evaluate its characteristics. Two kinds of DMDsp, namely system-based DMDsp (sDMDsp) and observation-based DMDsp (oDMDsp), combined with three kinds of optimization algorithm, namely the fast iterative shrinkage thresholding algorithm (FISTA), the alternating direction method of multipliers (ADMM), and a greedy algorithm, are investigated. For both sDMDsp and oDMDsp, FISTA yields the shortest processing time. The processing time for sDMDsp with FISTA is shorter than that for oDMDsp with FISTA. The original data reconstruction errors for sDMDsp and oDMDsp are similar among the three optimization algorithms. The noise robustness for sDMDsp and oDMDsp is evaluated. sDMDsp and oDMDsp have similar robustness to observation noise, except for a system with large system and observation noise, for which oDMDsp outperforms sDMDsp.

A New L₁ Multi-Kernel Learning Support Vector Regression Ensemble Algorithm With AdaBoost

This paper proposes a new multi-kernel learning ensemble algorithm, called Ada-<inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>MKL-WSVR, which can be regarded as an extension of multi-kernel learning (MKL) and weighted support vector regression (WSVR). The first novelty is to add the <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm of the weights of the combined kernel function to the objective function of WSVR, which is used to adaptively select the optimal base models and their parameters. In addition, an accelerated method based on fast iterative shrinkage thresholding algorithm (FISTA) is developed to solve the weights of the combined kernel function. The second novelty is to propose an integrated learning framework based on AdaBoost, named Ada-<inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>MKL-WSVR. In this framework, we integrate FISTA into AdaBoost. At each iteration, we optimize the weights of the combined kernel function and update the weights of the training samples at the same time. Then an ensemble regression function of a set of regression functions is output. Finally, two groups of the experiments are designed to verify the performance of our algorithm. On the first group of the experiments including eight datasets from UCI machine learning repository, the MAEs and RMSEs of Ada-<inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>MKL-WSVR are reduced by 11.14&#x0025; and 9.08&#x0025; on average, respectively. Furthermore, on the second group of the experiments including the COVID-19 epidemic datasets from eight countries, the MAEs and RMSEs of Ada-<inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula>MKL-WSVR are reduced by 31.19&#x0025; and 29.98&#x0025; on average, respectively.

Online Tensor Robust Principal Component Analysis

Online robust principal component analysis (RPCA) algorithms recursively decompose incoming data into low-rank and sparse components. However, they operate on data vectors and cannot directly be applied to higher-order data arrays (e.g. video frames). In this paper, we propose a new online robust PCA algorithm that preserves the multi-dimensional structure of data. Our algorithm is based on the recently proposed tensor singular value decomposition (T-SVD). We develop a convex optimization-based approach to recover the sparse component; and subsequently, update the low-rank component using incremental T-SVD. We propose an efficient tensor convolutional extension to the fast iterative shrinkage thresholding algorithm (FISTA) to produce a fast algorithm to solve this optimization problem. We demonstrate tensor-RPCA with the application of background foreground separation in a video stream. The foreground component is modeled as a sparse signal. The background component is modeled as a gradually changing low-rank subspace. Extensive experiments on real-world videos are presented and results demonstrate the effectiveness of our online tensor robust PCA.

Image Reconstruction for Low-Oversampled Staggered SAR via HDM-FISTA

Due to the unequispaced pulse repetition interval (PRI), the low-oversampling ratio and the range-variant blockage, the echo of the low-oversampled staggered SAR (LS-SAR) is nonuniformly sampled with sub-Nyquist and range-variant rate. However, the existing LS-SAR processing methods lack robustness with regards to the scenario type and the PRI variation mode. In this article, a compressive-sensing-based image reconstruction method for the LS-SAR is proposed. First, a hybrid-domain model (HDM) of the LS-SAR echo is presented. In the HDM, the coupled range cell migration (RCM), the unequispaced PRI, and the conflict blockage are formulated as the matrix multiplications with a 3-D tensor, a 2-D matrix, and a Hadamard product, respectively. Based on the HDM, the image reconstruction is realized through the 2-D fast iterative shrinkage thresholding algorithm (ISTA), in which the gradient is derived by exploiting the properties of the tensor and matrix trace. The fast Fourier transform (FFT) and the nonuniform FFT are implemented to accelerate the computation. Due to good accommodation of the RCM and the LS-SAR sampling characteristics, the proposed method can work well for various PRI variation modes and scenario types. Simulations using the point scatter and the distributed target with wide-swath extension demonstrate the effectiveness as well as the robustness of the proposed method.

Compressed Sensing Image Reconstruction of Ultrasound Image for Treatment of Early Traumatic Myositis Ossificans of Elbow Joint by Electroacupuncture.

This article conducts a retrospective analysis of 500 patients with posttraumatic elbow dysfunction admitted to our department from March 2019 to September 2020. The average time from injury to operation is 11 months (2–20 months). We adopt a personalized treatment method to completely remove the hyperplastic adhesion tissue and heterotopic ossification around the joint, remove part of the joint capsule and ligament, and release it to achieve maximum function. After the operation, an external fixator was used to stabilize the loosened elbow joint, and the patient was guided to perform rehabilitation exercises with the aid of a hinged external fixator, and celecoxib was used to prevent heterotopic ossification. Mayo functional scoring system was used to evaluate the curative effect before and after surgery. The rapid realization of ultrasound imaging under the framework of compressed sensing is studied. Under the premise of ensuring the quality of ultrasound imaging reconstruction, the theory of ultrasound imaging is improved, and a plane wave acoustic scattering ultrasound echo model is established. On this basis, the theory of compressed sensing is introduced, the mathematical model of compressed sensing reconstruction is established, and the fast iterative shrinkage thresholding algorithm (FISTA) of compressed sensing reconstruction is improved to reduce the computational complexity and the number of iterations. This article uses FISTA directly to reconstruct medical ultrasound images, and the reconstruction results are not ideal. Therefore, a simulation model of FISTA training and testing was established using the standard image library. By adding different intensities of noise to all images in the image library, the influence of noise intensity on the quality of FISTA reconstructed images is analyzed, and it is found that the FISTA model has requirements for the quality of the images to be reconstructed and the training set images. In this paper, Rob's blind deconvolution restoration algorithm is used to preprocess the original ultrasound image. The clarity of the texture details of the restored ultrasound image is significantly improved, and the image quality is improved, which meets the above requirements. This paper finally formed a reconstruction model suitable for ultrasound images. The reconstruction strategy verified by the ultrasound images provided by the Institute of Ultrasound Imaging of a medical university has achieved a significant improvement in the quality of ultrasound images.

An improved fast iterative shrinkage thresholding algorithm with an error for image deblurring problem

In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters such that another strong convergence theorem for these problem is obtained. We also apply our main result to improve the fast iterative shrinkage thresholding algorithm (IFISTA) with an error for solving the image deblurring problem. Finally, we provide numerical experiments to illustrate the convergence behavior and show the effectiveness of the sequence constructed by the inertial technique to the fast processing with high performance and the fast convergence with good performance of IFISTA.

FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging

Inverse problems are essential to imaging applications. In this letter, we propose a model-based deep learning network, named FISTA-Net, by combining the merits of interpretability and generality of the model-based Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) and strong regularization and tuning-free advantages of the data-driven neural network. By unfolding the FISTA into a deep network, the architecture of FISTA-Net consists of multiple gradient descent, proximal mapping, and momentum modules in cascade. Different from FISTA, the gradient matrix in FISTA-Net can be updated during iteration and a proximal operator network is developed for nonlinear thresholding which can be learned through end-to-end training. Key parameters of FISTA-Net including the gradient step size, thresholding value and momentum scalar are tuning-free and learned from training data rather than hand-crafted. We further impose positive and monotonous constraints on these parameters to ensure they converge properly. The experimental results, evaluated both visually and quantitatively, show that the FISTA-Net can optimize parameters for different imaging tasks, i.e. Electromagnetic Tomography (EMT) and X-ray Computational Tomography (X-ray CT). It outperforms the state-of-the-art model-based and deep learning methods and exhibits good generalization ability over other competitive learning-based approaches under different noise levels.

Improved atmospheric weighted mean temperature modeling using sparse kernel learning

As a crucial parameter in the process of converting the zenith wet delay into precipitable water vapor at Global Navigation Satellite System (GNSS) stations, the weighted mean temperature (Tm) influences the accuracy of GNSS-based water vapor retrievals. We propose an improved atmospheric Tm modeling method by introducing sparse kernel learning to obtain high-accuracy and high-temporal-resolution Tm data. To establish the model, the temporal variation characteristics of Tm time series are first analyzed by spectral analysis using the Lomb–Scargle periodogram. Second, the sparse kernel learning method is introduced to model the residuals from spectral analysis, for which the Gauss radial basis function kernel, L1-norm regularization, and the highly efficient fast iterative shrinkage thresholding algorithm are employed. To verify the performance of the proposed method, we used ERA5 hourly data from China’s 9 International GNSS Service stations produced by the European Centre for Medium-Range Weather Forecasts. ERA5 Tm data with a temporal resolution of 12 h are used as the training data, and the ERA5 hourly Tm data (excluding the data employed for modeling) are used for testing. The results show that compared with the spectral analysis accuracy, the accuracy of the calculated Tm can be improved by approximately 48.3% when the residual sparse kernel learning method is used. Thus, this proposed method for GNSS-based water vapor retrievals can provide high-accuracy and high-temporal-resolution Tm data.