A Huber Function based Restoration Algorithm for Astronomy Image Compression

In image denoising, in order to overcome the shortcoming that the uniform wavelet threshold in iterative thresholding algorithm can't separate the image from noise effectively at each iteration leads to the quality of the reconstructed image is poor, an improved curvelet threshold is proposed to replace it. And then iterative curvelet thresholding algorithm based on the improved threshold is proposed. In this paper, we apply the proposed algorithm for high resolution astronomical image denoising. The experimental result shows that the proposed algorithm improves the visual quality, effectively protects astronomical image details. When compression ratio is lower, the proposed algorithm still can obtain a higher peak signal to noise ratio (PSNR).

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.

ABSTRACTTo improve the image quality of terahertz (THz) continuous wave (CW) computed tomography (CT) under sparse‐view projections, a sparse‐view adaptive‐weighted Bregman Huber total variation (AW‐BHTV) method is proposed and experimentally evaluated at 0.11 THz. The Huber function is served as the fidelity term and TV function is worked for the regularization term, optimized by the adaptive weights, incorporating with iterative algorithms containing the modified simultaneous algebraic reconstruction technique (MSART) and the iterative filtered back‐projection (FBP). Sparse‐view reconstruction experiments are carefully implemented via polystyrene (PS) foam samples: Sample 1 and Sample 2, respectively. Under 20 projection angles by MSART based AW‐BHTV, the values of rooted mean‐square‐error (RMSE), peak signal‐to‐noise ratio (PSNR), structure similarity (SSIM) and feature similarity (FSIM) are 0.0061, 22.1427, 0.8738 and 0.9902 for Sample 1 together with 0.0051, 22.9101, 0.8376 and 0.9885 for Sample 2 separately. All of the results above suggest that the proposed AW‐BHTV method can effectively protect image details and strengthen image quality in sparse‐view THz CW CT.

Quality is a very important parameter for all objects and their functionalities. In image-based object recognition, image quality is a prime criterion. For authentic image quality evaluation, ground truth is required. But in practice, it is very difficult to find the ground truth. Usually, image quality is being assessed by full reference metrics, like MSE (Mean Square Error) and PSNR (Peak Signal to Noise Ratio). In contrast to MSE and PSNR, recently, two more full reference metrics SSIM (Structured Similarity Indexing Method) and FSIM (Feature Similarity Indexing Method) are developed with a view to compare the structural and feature similarity measures between restored and original objects on the basis of perception. This paper is mainly stressed on comparing different image quality metrics to give a comprehensive view. Experimentation with these metrics using benchmark images is performed through denoising for different noise concentrations. All metrics have given consistent results. However, from representation perspective, SSIM and FSIM are normalized, but MSE and PSNR are not; and from semantic perspective, MSE and PSNR are giving only absolute error; on the other hand, SSIM and PSNR are giving perception and saliency-based error. So, SSIM and FSIM can be treated more understandable than the MSE and PSNR.

Objective. Computed tomography (CT) and magnetic resonance imaging (MRI) are widely used in medical imaging modalities, and provide valuable information for clinical diagnosis and treatment. However, due to hardware limitations and radiation safety concerns, the acquired images are often limited in resolution. Super-resolution reconstruction (SR) techniques have been developed to enhance the resolution of CT and MRI slices, which can potentially improve diagnostic accuracy. To capture more useful feature information and reconstruct higher quality super-resolution images, we proposed a novel hybrid framework SR model based on generative adversarial networks. Approach. The proposed SR model combines frequency domain and perceptual loss functions, which can work in both frequency domain and image domain (spatial domain). The proposed SR model consists of 4 parts: (i) the discrete Fourier transform (DFT) operation transforms the image from the image domain to frequency domain; (ii) a complex residual U-net performs SR in the frequency domain; (iii) the inverse discrete Fourier transform (iDFT) operation based on data fusion transforms the image from the frequency domain to image domain; (iv) an enhanced residual U-net network is used for SR of image domain. Main results. Experimental results on bladder MRI slices, abdomen CT slices, and brain MRI slices show that the proposed SR model outperforms state-of-the-art SR methods in terms of visual quality and objective quality metric such as the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR), which proves that the proposed model has better generalization and robustness. (Bladder dataset: upscaling factor of 2: SSIM = 0.913, PSNR = 31.203; upscaling factor of 4: SSIM = 0.821, PSNR = 28.604. Abdomen dataset: upscaling factor of 2: SSIM = 0.929, PSNR = 32.594; upscaling factor of 4: SSIM = 0.834, PSNR = 27.050. Brain dataset: SSIM = 0.861, PSNR = 26.945). Significance. Our proposed SR model is capable of SR for CT and MRI slices. The SR results provide a reliable and effective foundation for clinical diagnosis and treatment.

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.

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.

Compressed sensing (CS) is a novel developed theoretical framework for information acquisition and processing. Taking advantages of the sparsity or compressibility inherent in real world signals, CS can collect compressed data at the sampling rate much lower than that needed in Shannon's theorem. When it has been used for medical imaging techniques, CS theory can fast the scanning speed of MRI, reduce the radiation doses and alleviate the patients' suffering. In order to obtain the effective sparse representation, the nonsubsampled contourlet transform in the frequency domain (NSCT-FD) is adopted, then an improved fast iterative soft thresholding algorithm (FISTA) is applied for CS-MRA reconstruction. This novel method not only inherits the simplicity and effectiveness of the original FISTA, and the sparse curvy representation ability of the contourlet transform, but also has the advantages of the shift-invariant property and much less computational burden. The performance is evaluated qualitatively and quantitatively both in noiseless and noisy situations, compared to the classic wavelet and the sharp frequency localization contourlet transform (SFLCT) method. Three quantitative indices are employed including the peak signal to noise ratio (PSNR), mutual information (MI) and relative l 2 norm error (RLNE) and qualitative performance evaluations use the profiles in horizontal direction and local region magnification comparison. Experimental results demonstrate the superiority of the NSCT-FD algorithm, displaying higher PSNR and MI, and lower RLNE indices in both noiseless and noisy MRA images, which have good reconstruction accuracy with reasonable real time computation speed. It is manifest that the NSCT-FD algorithm can be applied in fast medical imaging fields to achieve quality images in a relatively fast process, which will benefit cardiac and carotid MRI, dynamic MRI and MRA.

In recent years, extensive research has shown that deep learning-based compressed image reconstruction algorithms can achieve faster and better high-quality reconstruction for single-pixel imaging, and that reconstruction quality can be further improved by joint optimization of sampling and reconstruction. However, these network-based models mostly adopt end-to-end learning, and their structures are not interpretable. In this paper, we propose SRMU-Net, a sampling and reconstruction jointly optimized model unfolding network. A fully connected layer or a large convolutional layer that simulates compressed reconstruction is added to the compressed reconstruction network, which is composed of multiple cascaded iterative shrinkage thresholding algorithm (ISTA) unfolding iteration blocks. To achieve joint optimization of sampling and reconstruction, a specially designed network structure is proposed so that the sampling matrix can be input into ISTA unfolding iteration blocks as a learnable parameter. We have shown that the proposed network outperforms the existing algorithms by extensive simulations and experiments.

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.