Clutter Suppression for Radar via Deep Joint Sparse Recovery Network

Low-rank prior-based Fast-RPCA for clutter filtering and noise suppression in non-contrast ultrasound microvascular imaging

<sec>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.</sec><sec>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 <i>α</i> on the result is then investigated, and it is found that when <i>α</i> = 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.</sec><sec>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.</sec>

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.

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.

Effective clutter filtering is essential for ultrafast ultrasound small blood flow imaging, where weak blood flow signals are often obscured by tissue clutter and noise. While singular value decomposition (SVD)-based methods are widely used, their performance is limited by overlapping singular value distributions between blood flow, clutter, and noise. This study proposes a Cauchy-norm-based sparse SVD (S-SVD) clutter filtering method that integrates a sparsity penalty into the classical SVD framework. By leveraging the structural sparsity of blood flow, the method employs a Cauchy norm regularization to suppress noise while preserving small vessel details. A randomized spatial downsampling strategy is further used to increase computational efficiency. The proposed method is validated through simulated and in vivo rat brain experiments, demonstrating superior performance in power Doppler imaging and functional ultrasound (fUS) imaging compared to conventional SVD and robust principal component analysis (RPCA). Results show significant improvements in signal-tonoise ratio (SNR) by about 10dB and contrast-to-noise ratio (CNR) by about 9dB, with enhanced visualization of small vascular networks and dynamic cerebral blood volume (CBV) responses to whisker stimulation. Future work will focus on accelerating optimization and integrating deconvolution for further resolution enhancement.

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.

Solving optimization problems with sparse or low-rank optimal solutions has been an important topic since the recent emergence of compressed sensing and its matrix extensions such as the matrix rank minimization and robust principal component analysis problems. Compressed sensing enables one to recover a signal or image with fewer observations than the “length” of the signal or image, and thus provides potential breakthroughs in applications where data acquisition is costly. However, the potential impact of compressed sensing cannot be realized without efficient optimization algorithms that can handle extremely large-scale and dense data from real applications. Although the convex relaxations of these problems can be reformulated as either linear programming, second-order cone programming or semidefinite programming problems, the standard methods for solving these relaxations are not applicable because the problems are usually of huge size and contain dense data. In this dissertation, we give efficient algorithms for solving these “sparse” optimization problems and analyze the convergence and iteration complexity properties of these algorithms. Chapter 2 presents algorithms for solving the linearly constrained matrix rank minimization problem. The tightest convex relaxation of this problem is the linearly constrained nuclear norm minimization. Although the latter can be cast and solved as a semidefinite programming problem, such an approach is computationally expensive when the matrices are large. In Chapter 2, we propose fixed-point and Bregman iterative algorithms for solving the nuclear norm minimization problem and prove convergence of the first of these algorithms. By using a homotopy approach together with an approximate singular value decomposition procedure, we get a very fast, robust and powerful algorithm, which we call FPCA (Fixed Point Continuation with Approximate SVD), that can solve very large matrix rank minimization problems. Our numerical results on randomly generated and real matrix completion problems demonstrate that this algorithm is much faster and provides much better recoverability than semidefinite programming solvers such as SDPT3. For example, our algorithm can recover 1000 × 1000 matrices of rank 50 with a relative error of 10−5 in about 3 minutes by sampling only 20 percent of the elements. We know of no other method that achieves as good recoverability. Numerical experiments on online recommendation, DNA microarray data set and image inpainting problems demonstrate the effectiveness of our algorithms. In Chapter 3, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed sensing. Numerical results for these algorithms for solving linearly constrained matrix rank minimization problems are reported. Chapters 4 and 5 considers alternating direction type methods for solving composite convex optimization problems. We present in Chapter 4 alternating linearization algorithms that are based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most O(1/e) iterations to obtain an e-optimal solution, while our accelerated (i.e., fast) versions require at most O(1/ 3 ) iterations, with little change in the computational effort required at each iteration. For more general problem, i.e., minimizing the sum of K convex functions, we propose multiple-splitting algorithms for solving them. We propose both basic and accelerated algorithms with O(1/e) and O(1/ 3 ) iteration complexity bounds for obtaining an e-optimal solution. To the best of our knowledge, the complexity results presented in these two chapters are the first ones of this type that have been given for splitting and alternating direction type methods. Numerical results on various applications in sparse and low-rank optimization, including compressed sensing, matrix completion, image deblurring, robust principal component analysis, are reported to demonstrate the efficiency of our methods.

Chaos through-wall imaging radar has attracted wide attention due to its inherent low probability of detection/interception, strong anti-jamming, and high resolution. However, the target response is usually overwhelmed by strong clutter. This paper proposes an imaging-then-decomposition method based on two-stage robust principal component analysis (RPCA) to remove the clutter and recover the target image. The proposed method firstly focuses the energy of the preprocessing data by the back-projection imaging algorithm; then, it performs matrix decomposition on the full and the sparse component of the focused data, in succession, by the RPCA algorithm. Simulation and experimental results show that the proposed method can suppress the clutter dramatically and indicate human targets distinctly. Compared with the traditional methods, it has effectiveness and superiority in improving the signal-to-clutter ratio.

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 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.

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.

Statistical iterative reconstruction in Cone-beam computed tomography (CBCT) uses prior knowledge to form different kinds of regularization terms. The total variation (TV) regularization has shown state-of-the-art performance in suppressing noises and preserving edges. However, it produces the well-known staircase effect. In this paper, a method that involves second-order differential operators was employed to avoid the staircase effect. The ability to avoid staircase effect lies in that higher-order derivatives can avoid over-sharpening the regions of smooth intensity transitions. Meanwhile, a fast iterative shrinkage-thresholding algorithm was used for the corresponding optimization problem. The proposed Hessian Schatten norm-based regularization keeps lots of favorable properties of TV, such as translation and scale invariant, with getting rid of the staircase effect that appears in TV-based reconstructions. The experiments demonstrated the outstanding ability of the proposed algorithm over TV method especially in suppressing the staircase effect.

The “fast iterative shrinkage-thresholding algorithm,” a.k.a. FISTA, is one of the most well known first-order optimization scheme in the literature, as it achieves the worst-case $O(1/k^2)$ optimal convergence rate for objective function value. However, despite such an optimal theoretical convergence rate, in practice the (local) oscillatory behavior of FISTA often damps its efficiency. Over the past years, various efforts have been made in the literature to improve the practical performance of FISTA, such as monotone FISTA, restarting FISTA, and backtracking strategies. In this paper, we propose a simple yet effective modification to the original FISTA scheme which has two advantages: It allows us to (1) prove the convergence of generated sequence and (2) design a so-called lazy-start strategy which can be up to an order faster than the original scheme. Moreover, we propose novel adaptive and greedy strategies which further improve the practical performance. The advantages of the proposed schemes are tested through problems arising from inverse problems, machine learning, and signal/image processing.