Synthetic aperture radar (SAR) typically faces both large-scale data and speckle noise problems, which, respectively, induce enormous strains on transmission and storage and interfere with the analysis and interpretation of SAR images. To tackle these, we present a real-time processing deep network, called SPB-Net, to implement imaging and speckle suppression simultaneously. First, a novel imaging-despeckling observation model with the nonlogarithmic additive speckle noise is established. Subsequently, guided by the statistical properties of noise and sparse and detail-preserved requirements in SAR imaging and despeckling, we formulate an $L_{2}$ along with two $L_{1}$ regularizations as the fidelity, sparse, and image detail-preserved constraints, respectively. Convolution layers are employed to improve the feature representation capability in the latter $L_{1}$ term as well. Based on this, we construct a corresponding convex optimization problem. Then, the complex-valued split Bregman method, focusing on the complex-variable convex problem, is unfolded into a parameter-learnable and architecture-fixed SPB-Net to solve the proposed problem effectively and efficiently. Experimental results with the downsampled Radarsat-1 raw data demonstrate the validity in imaging and speckle suppression and the real-time processing capability of the proposed SPB-Net.

The Split Bregman method (SBM), a popular and universal CS reconstruction algorithm for inverse problems with both l₁-norm and TV-norm regularization, has been extensively applied in complex domains through the complex-to-real transforming technique, e.g., MRI imaging and radar. However, SBM still has great potential in complex applications due to the following two points; Bregman Iteration (BI), employed in SBM, may not make good use of the phase information for complex variables. In addition, the converting technique may consume more time. To address that, this paper presents the complex-valued Split Bregman method (CV-SBM), which theoretically generalizes the original SBM into the complex domain. The complex-valued Bregman distance (CV-BD) is first defined by replacing the corresponding regularization in the inverse problem. Then, we propose the complex-valued Bregman Iteration (CV-BI) to solve this new problem. How well-defined and the convergence of CV-BI are analyzed in detail according to the complex-valued calculation rules and optimization theory. These properties prove that CV-BI is able to solve inverse problems if the regularization is convex. Nevertheless, CV-BI needs the help of other algorithms for various kinds of regularization. To avoid the dependence on extra algorithms and simplify the iteration process simultaneously, we adopt the variable separation technique and propose CV-SBM for resolving convex inverse problems. Simulation results on complex-valued l₁-norm problems illustrate the effectiveness of the proposed CV-SBM. CV-SBM exhibits remarkable superiority compared with SBM in the complex-to-real transforming technique. Specifically, in the case of large signal scale n = 512, CV-SBM yields 18.2%, 17.6%, and 26.7% lower mean square error (MSE) as well as takes 28.8%, 25.6%, and 23.6% less time cost than the original SBM in 10 dB, 15 dB, and 20 dB SNR situations, respectively.

Large quantities of sampling data and speckle noise are two serious problems existing in synthetic aperture radar (SAR). The former puts enormous strain on data measurement, transmission, and storage. The latter deteriorates imaging quality, disturbing the subsequent processing in SAR systems. This study proposes a real-time deep network to address these issues. The proposed network is able to concurrently achieve SAR imaging and despeckling with down-sampled data. Specifically, to fit more diverse imaging regions, we suppose that the noise in the SAR imaging-despeckling observation model follows a universal complex generalized Gaussian distribution. Based on this assumption, an optimization problem with a convex $L_{q}$ -norm ( $q >$ 1) fidelity term is constructed through the maximum $a$ posteriori (MAP) estimation. We employ an $L_{1}$ -norm sparse constraint and a convolutional neural networks (CNNs) projection-based detail preservation constraint to further promote the imaging and speckle reduction capabilities. Then, the complex-valued split Bregman method (CV-SBM) is applied to convert the proposed problem into an equivalent sequence of sub-problems. We devise a computationally efficient solution for the fidelity term-related sub-problem, due to the specific down-sampled strategy in SAR. A substitutive cost function and a CNN structure are introduced to solve the projection-related sub-problem. Finally, the iterative steps of CV-SBM are cast into a deep network-dubbed $L_{q}$ -split Bregman (SPB)-Net to yield a desirable imaging and despeckling result within a small number of iterations. Numerical experiments based on the real Radarsat-1 data validate the efficiency and feasibility of the proposed $L_{q}$ -SPB-Net in real-time imaging and despeckling with down-sampled data.

Synthetic aperture radar (SAR) generally suffers from enormous strains from large quantities of sampling data and serious interferences from the speckle noise. This letter proposes a novel deep network to address these problems. By utilizing the prior knowledge in a more reasonable way, the proposed network could realize SAR imaging and despeckling with down-sampled data simultaneously. Specifically, we decompose the SAR image in the SAR imaging-despeckling observation model into a sparse matrix and a low-rank matrix, and then establish an optimization problem with the corresponding sparse and low-rank priors. Moreover, the deep convolutional neural networks (CNN) denoiser prior is also introduced to further improve the speckle reduction capability. Then, we devise a deep network called SLRCP-Net to solve this problem. Experiments conducted on real Radarsat-1 down-sampled data demonstrate the validity of SLRCP-Net in SAR imaging and speckle suppression.

Signal detection and classification tasks, especially in the realm of audio, suffer from difficulties in capturing long short-term dependencies and effectively utilizing samples. Firstly, audio signal detection and classification need to classify audio signals and detect their onset and offset times; therefore, obtaining long short-term dependencies is necessary. The methods based on RNNs have high time complexity and dilated convolution-based methods suffer from the “gridding issue” challenge; thus, the HDC-Inception module is proposed to efficiently extract long short-term dependencies. Combining the advantages of the Inception module and a hybrid dilated convolution (HDC) framework, the HDC-Inception module can both alleviate the “gridding issue” and obtain long short-term dependencies. Secondly, datasets have large numbers of silent segments and too many samples for some signal types, which are redundant and less difficult to detect, and, therefore, should not be overly prioritized. Thus, selecting effective samples and guiding the training based on them is of great importance. Inspired by support vector machine (SVM), combining soft margin SVM and cross-entropy loss (CE loss), the soft margin CE loss is proposed. Soft margin CE loss can adaptively select support vectors (effective samples) in datasets and guide training based on the selected samples. To utilize datasets more sufficiently, a hybrid CE loss is proposed. Using the benefits of soft margin CE loss and CE loss, hybrid CE loss guides the training with all samples and gives weight to support vectors. Soft margin CE loss and hybrid CE loss can be extended to most classification tasks and offer a wide range of applications and great potential.