Overview of compressed sensing: Sensing model, reconstruction algorithm, and its applications

With the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist-Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials. © 2020 by the authors

Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes

This paper discusses the performance and cost of two computationally efficient Fourier-based tomographic wavefront reconstruction algorithms for wide-field laser guide star (LGS) adaptive optics (AO). The first algorithm is the iterative Fourier domain preconditioned conjugate gradient (FDPCG) algorithm developed by Yang et al. [Appl. Opt. 45, 5281 (2006)], combined with pseudo-open-loop control (POLC). FDPCG’s computational cost is proportional to N log(N), where N denotes the dimensionality of the tomography problem. The second algorithm is the distributed Kalman filter (DKF) developed by Massioni et al. [J. Opt. Soc. Am. A 28, 2298 (2011)], which is a noniterative spatially invariant controller. When implemented in the Fourier domain, DKF’s cost is also proportional to N log(N). Both algorithms are capable of estimating spatial frequency components of the residual phase beyond the wavefront sensor (WFS) cutoff frequency thanks to regularization, thereby reducing WFS spatial aliasing at the expense of more computations. We present performance and cost analyses for the LGS multiconjugate AO system under design for the Thirty Meter Telescope, as well as DKF’s sensitivity to uncertainties in wind profile prior information. We found that, provided the wind profile is known to better than 10% wind speed accuracy and 20 deg wind direction accuracy, DKF, despite its spatial invariance assumptions, delivers a significantly reduced wavefront error compared to the static FDPCG minimum variance estimator combined with POLC. Due to its nonsequential nature and high degree of parallelism, DKF is particularly well suited for real-time implementation on inexpensive off-the-shelf graphics processing units

Convolutional Sparse Support Estimator Network (CSEN) : From Energy-Efficient Support Estimation to Learning-Aided Compressive Sensing

Support estimation (SE) of a sparse signal refers to finding the location indices of the nonzero elements in a sparse representation. Most of the traditional approaches dealing with SE problems are iterative algorithms based on greedy methods or optimization techniques. Indeed, a vast majority of them use sparse signal recovery (SR) techniques to obtain support sets instead of directly mapping the nonzero locations from denser measurements (e.g., compressively sensed measurements). This study proposes a novel approach for learning such a mapping from a training set. To accomplish this objective, the convolutional sparse support estimator networks (CSENs), each with a compact configuration, are designed. The proposed CSEN can be a crucial tool for the following scenarios: 1) real-time and low-cost SE can be applied in any mobile and low-power edge device for anomaly localization, simultaneous face recognition, and so on and 2) CSEN’s output can directly be used as “prior information,” which improves the performance of sparse SR algorithms. The results over the benchmark datasets show that state-of-the-art performance levels can be achieved by the proposed approach with a significantly reduced computational complexity.publishedVersionPeer reviewe

Reflection Mode Diffraction Tomography

In the field of ultrasound diffraction tomography, a cross section of a weakly scattering object is reconstructed from measurements of the sound scattered from the insonified object. This research studies tomographic imaging algorithms that deal only with the sound that is backscattered from the object. The use of the backscattered sound provides higher resolution reconstructions due to the higher spatial frequency information about the object that is obtained from the backscatter. Unfortunately the cost of the high frequency information contained in the backscatter is the loss of low frequency information. Different approaches to compensate for this loss are discussed. An additional benefit of reflection mode tomography is that it has the advantage of requiring only 180° access to the object whereas transmission mode requires 360°. The charter of this research is to explore the effectiveness of current reflection mode diffraction tomography algorithms and to theoretically develop, as well as experimentally verify, new algorithms. Different scanning geometries with different methods of insonification are explored. Many different approaches to the analysis of the problem are taken

Non-iterative and Fast Deep Learning: Multilayer Extreme Learning Machines

In the past decade, deep learning techniques have powered many aspects of our daily life, and drawn ever-increasing research interests. However, conventional deep learning approaches, such as deep belief network (DBN), restricted Boltzmann machine (RBM), and convolutional neural network (CNN), suffer from time-consuming training process due to fine-tuning of a large number of parameters and the complicated hierarchical structure. Furthermore, the above complication makes it difficult to theoretically analyze and prove the universal approximation of those conventional deep learning approaches. In order to tackle the issues, multilayer extreme learning machines (ML-ELM) were proposed, which accelerate the development of deep learning. Compared with conventional deep learning, ML-ELMs are non-iterative and fast due to the random feature mapping mechanism. In this paper, we perform a thorough review on the development of ML-ELMs, including stacked ELM autoencoder (ELM-AE), residual ELM, and local receptive field based ELM (ELM-LRF), as well as address their applications. In addition, we also discuss the connection between random neural networks and conventional deep learning