Sampling and Reconstruction Jointly Optimized Model Unfolding Network for Single-Pixel Imaging

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze‐and‐excitation mechanisms into the ISTA block. This block serves as a deep equilibrium layer connected to a semi‐tensor product network for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC‐DEQ‐Net, exhibits competitive performance compared to state‐of‐the‐art network‐based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC‐DEQ‐Net can be iteratively used, gradually improving reconstruction accuracy while considering computation tradeoffs. Additionally, the model benefits from multiscale dilated convolutions, further enhancing performance.

The most common technique for generating B-mode ultrasound (US) images is delay-and-sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently, we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real time. In this article, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, which is based on unfolding the iterative shrinkage thresholding algorithm (ISTA), resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high-quality imaging performance. Using in vivo data, we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.

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.

Synthetic aperture radar tomography (TomoSAR) has been widely employed in 3-D urban mapping. However, state-of-the-art super-resolving TomoSAR algorithms are computationally expensive, because conventional numerical solvers need to solve the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2^{-}}l_{1}$</tex> mix norm minimization. This paper proposes a computationally efficient super-resolving To-moSAR inversion algorithm based on deep learning. We studied the potential of deep learning to mimic a conventional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2}-l_{1}$</tex> mix norm solver, i.e. iterative shrinkage thresholding algorithm (ISTA), and proposed several improvements of the complex-valued learned ISTA for TomoSAR inversion. Investigation on the super-resolution ability and estimator efficiency of the proposed algorithm shows that the proposed algorithm approaches the Cramer Rao lower bound (CRLB) with a computational efficiency more than 100 times better than the conventional solver.

Compressed sensing (CS) reconstruction of nonsparse scenes is one of the difficulties in synthetic aperture radar (SAR) imaging technology. Although the conventional CS method with sparse representation has proven applicable for nonsparse SAR reconstruction, its disadvantages are unsatisfactory imaging quality and high computational complexity under downsampling. In this paper, a novel deep learning approach for nonsparse SAR scene reconstruction is proposed based on sparse representation and the iterative shrinkage threshold algorithm (ISTA). Specifically, we first develop a sparse representation-based imaging model associated with the &#x2113;₁ sparse regularizer in nonlinear transform domains. Then, the advantages of the recurrent neural network (RNN) and convolutional neural network (CNN) are incorporated into an ISTA-inspired deep unfolded network (DUN) called SR-ISTA-Net, in which all the parameters are layer-varied rather than handcrafted. The experiments verify that the proposed SR-ISTA-Net can provide high-quality reconstruction results under nonsparse scenes while substantially reducing imaging time.

We present two model-based neural network architectures purposed for sporadic user detection and channel estimation in massive machine-type communications. In the scenario under consideration, a base station assigns the users a set of pilot sequences that is linearly dependent, but because user activity is sporadic the detection/estimation problem is amenable to sparse recovery algorithms. Further, we consider a millimeter-wave wireless channel, so that the channel vectors are sparse in a known dictionary. We apply the deep unfolding framework to design custom neural network layers by unrolling two iterative optimization algorithms: (1) linearized alternating direction method of multipliers, which we apply to a constrained convex problem, and (2) vector approximate message passing featuring a novel denoiser based on the iterative shrinkage thresholding algorithm. The networks thus inherit domain knowledge as encapsulated by the signal model, and suitable operations as informed by the algorithms—in the same spirit as convolutional networks that exploit structure inherent in images and audio, except grounded in optimization and statistics. The networks, trained on synthetic data generated from the block-fading millimeter-wave multiple access channel model, offer improved complexity and accuracy relative to their iterative counterparts, and are potentially a boon to cell-free MIMO systems.

In this paper, an image deconvolution problem using triangular wavelets is addressed. A simple blurred image is generated by the Gaussian-based blur kernel and additive Gaussian white noise. Two-dimensional orthogonal Haar wavelets on a triangular lattice, which gives sparse and isotropie representations of images, are selected as a dictionary. Using the iterative shrinkage threshold algorithm, some numerical experiments are carried out for the problem of recovering the original image from the noisy blurred image. We show that the triangular wavelets result in better performance than the conventional Haar wavelet transform.

The fast compressed sensing (CS) reconstruction for natural image processing aims to infer the original pixel vector from randomized measurements as correctly as possible. Current first-order proximal mainstream schemes, including alternating direction methods of multipliers (ADMM) and the iterative shrinkage thresholding algorithm (ISTA), have advantages in convergence and stability at the expense of computing speed and complex tuning strategy. This paper proposes the deep iterative shrinkage network for real-time applications, where network layers replace the iterative optimization steps. The hyperparameters associated with shrinkage thresholds and step sizes are adjusted by standard deep learning updates. Numerical results suggest that the proposed method has flexibility and effectiveness in image reconstruction with different compression ratios while preserving the computational simplicity of end-to-end methods.

This paper focuses on processing low oversampling echo data of staggered synthetic aperture radar (SAR). In staggered mode, the non-uniformly sampling and echo data loss cause severe azimuth ambiguity. To solve this problem, we propose a method combining the compressed sensing (CS) tool and the conformal Fourier transform (CFT) algorithm. First, the 2-D-fast iterative shrinkage thresholding algorithm (FISTA) is used to efficiently solve the optimization problem based on CS theory to recovery the missing data. Second, the CFT algorithm is used to accurately compute the spectrum of the non-uniformly sampled echo data. Unlike other methods suiting fast pulse repetition interval (PRI) change only, this method performs well for both fast and slow PRI change. Plus, the proposed method can be well applied to both point and distributed targets. Simulation results demonstrate that the proposed method can effectively and robustly suppress the azimuth ambiguity for staggered SAR data.

A new restoration algorithm based on Huber function for astronomy image compression was proposed in this paper. A combinatorial sensing matrix based on noiselet transform and subsample matrix was built for image acquisition. A restoration algorithm based on Huber function was introduced to reconstruct the signal. Peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used to evaluate the performance of the proposed algorithm. Compared with the standard compression algorithms, including JPEG and iterative shrinkage thresholding algorithm (ISTA) based reconstruction algorithm, the results obtained by the proposed algorithm are of higher structural similarity and PSNR. The proposed algorithm is suitable for the application scenarios of astronomy images with large data volume and high redundancy.

Sparse-representation-based synthetic aperture radar (SAR) imaging technology has shown superior potential in the reconstruction of nonsparse scenes. However, many existing compressed sensing (CS) methods with sparse representation cannot obtain an optimal sparse basis and only apply to the sensing matrix obtained by exact observation, resulting in a low image quality occupying more storage space. To reduce the computational cost and improve the imaging performance of nonsparse scenes, we formulate a deep learning SAR imaging method based on sparse representation and approximated observation deduced from the chirp-scaling algorithm (CSA). First, we incorporate the CSA-derived approximated observation model and a nonlinear transform function within a sparse reconstruction framework. Second, an iterative shrinkage threshold algorithm is adopted to solve this framework, and the solving process is unfolded as a deep SAR imaging network. Third, a dual-path convolutional neural network (CNN) block is designed in the network to achieve the nonlinear transform, dramatically improving the sparse representation capability over conventional transform-domain-based CS methods. Last, we improve the CNN block to develop an enhanced version of the deep SAR imaging network, in which all the parameters are layer-varied and trained by supervised learning. The experiments demonstrate that our proposed two imaging networks outperform conventional CS-driven and deep-learning-based methods in terms of computing efficiency and reconstruction performance of nonsparse scenes.

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.

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simple deep neural network (DNN) and developing a corresponding error backpropagation algorithm that allows to fine-tune the thresholding functions. Simulations on sparse statistical signals illustrate potential gains in estimation quality due to the proposed data adaptive ISTA.

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.

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.