scholarly journals An Efficient Nonconvex Regularization Method for Wavelet Frame Based Compressed Sensing Recovery

2021 ◽  
pp. 1-23
Author(s):  
Xiao-Juan Yang ◽  
Jin Jing
Keyword(s):  
Compressed Sensing ◽  
Numerical Experiment ◽  
Regularization Method ◽  
Optimization Problem ◽  
Tight Frame ◽  
Jel Classification ◽  
Adjustable Parameter ◽  
Convergence Speed ◽  
Wavelet Frame ◽  
Nonconvex Regularization

Abstract In this paper, we propose a variation model which takes advantage of the wavelet tight frame and nonconvex shrinkage penalties for compressed sensing recovery. We address the proposed optimization problem by introducing a adjustable parameter and a firm thresholding operations. Numerical experiment results show that the proposed method outperforms some existing methods in terms of the convergence speed and reconstruction errors. JEL classification numbers: 68U10, 65K10, 90C25, 62H35. Keywords: Compressed Sensing, Nonconvex, Firm thresholding, Wavelet tight frame.

An improved sparrow search algorithm based on levy flight and opposition-based learning

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Danni Chen ◽  
JianDong Zhao ◽  
Peng Huang ◽  
Xiongna Deng ◽  
Tingting Lu
Keyword(s):  
Parameter Optimization ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Convergence Speed ◽  
Support Vector ◽  
Lévy Flight ◽  
Levy Flight ◽  
Content Type ◽  
Opposition Based Learning

Purpose Sparrow search algorithm (SSA) is a novel global optimization method, but it is easy to fall into local optimization, which leads to its poor search accuracy and stability. The purpose of this study is to propose an improved SSA algorithm, called levy flight and opposition-based learning (LOSSA), based on LOSSA strategy. The LOSSA shows better search accuracy, faster convergence speed and stronger stability. Design/methodology/approach To further enhance the optimization performance of the algorithm, The Levy flight operation is introduced into the producers search process of the original SSA to enhance the ability of the algorithm to jump out of the local optimum. The opposition-based learning strategy generates better solutions for SSA, which is beneficial to accelerate the convergence speed of the algorithm. On the one hand, the performance of the LOSSA is evaluated by a set of numerical experiments based on classical benchmark functions. On the other hand, the hyper-parameter optimization problem of the Support Vector Machine (SVM) is also used to test the ability of LOSSA to solve practical problems. Findings First of all, the effectiveness of the two improved methods is verified by Wilcoxon signed rank test. Second, the statistical results of the numerical experiment show the significant improvement of the LOSSA compared with the original algorithm and other natural heuristic algorithms. Finally, the feasibility and effectiveness of the LOSSA in solving the hyper-parameter optimization problem of machine learning algorithms are demonstrated. Originality/value An improved SSA based on LOSSA is proposed in this paper. The experimental results show that the overall performance of the LOSSA is satisfactory. Compared with the SSA and other natural heuristic algorithms, the LOSSA shows better search accuracy, faster convergence speed and stronger stability. Moreover, the LOSSA also showed great optimization performance in the hyper-parameter optimization of the SVM model.

scholarly journals Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2568 ◽  
Author(s):  
Ruisong Wang ◽  
Gongliang Liu ◽  
Wenjing Kang ◽  
Bo Li ◽  
Ruofei Ma ◽  
...  
Keyword(s):  
Sensor Networks ◽  
Compressed Sensing ◽  
Bayesian Estimation ◽  
Sensor Node ◽  
Optimization Problem ◽  
Sensor Nodes ◽  
Underwater Sensor Networks ◽  
Node Selection ◽  
Selection Scheme ◽  
Error Covariance

Information acquisition in underwater sensor networks is usually limited by energy and bandwidth. Fortunately, the received signal can be represented sparsely on some basis. Therefore, a compressed sensing method can be used to collect the information by selecting a subset of the total sensor nodes. The conventional compressed sensing scheme is to select some sensor nodes randomly. The network lifetime and the correlation of sensor nodes are not considered. Therefore, it is significant to adjust the sensor node selection scheme according to these factors for the superior performance. In this paper, an optimized sensor node selection scheme is given based on Bayesian estimation theory. The advantage of Bayesian estimation is to give the closed-form expression of posterior density function and error covariance matrix. The proposed optimization problem first aims at minimizing the mean square error (MSE) of Bayesian estimation based on a given error covariance matrix. Then, the non-convex optimization problem is transformed as a convex semidefinite programming problem by relaxing the constraints. Finally, the residual energy of each sensor node is taken into account as a constraint in the optimization problem. Simulation results demonstrate that the proposed scheme has better performance than a conventional compressed sensing scheme.

Compressed-Sensing MRI Based on Adaptive Tight Frame in Gradient Domain

2018 ◽  
Vol 49 (5) ◽  
pp. 465-477 ◽  
Author(s):  
Xiaoyu Fan ◽  
Qiusheng Lian ◽  
Baoshun Shi
Keyword(s):  
Compressed Sensing ◽  
Tight Frame ◽  
Gradient Domain

CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING

2011 ◽  
Vol 09 (01) ◽  
pp. 79-110 ◽  
Author(s):  
GERLIND PLONKA ◽  
JIANWEI MA
Keyword(s):  
Compressed Sensing ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Split Bregman ◽  
Split Bregman Iteration ◽  
Special Cases ◽  
Sparsity Constraints ◽  
Iteration Methods ◽  
Wave Atoms ◽  
Sparsity Constrained Optimization

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ϵ with the measurement matrix Φ ∈ ℝK × N, K ≪ N, we consider a jointly sparsity-constrained optimization problem of the form [Formula: see text]. Here Ψc and Ψw are the transform matrices corresponding to the two frames, and the diagonal matrices Λc, Λw contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the Douglas–Rachford Split algorithm. Numerical experiments for compressed sensing-based Fourier-domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.

Image Reconstruction Based on Compressed Sensing with Split Bregman Algorithm and Fuzzy Bases

2012 ◽  
Vol 508 ◽  
pp. 80-83
Author(s):  
Jian Jiang Cui ◽  
Xu Jia ◽  
Jing Liu ◽  
Qi Li
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Original Data ◽  
Convergence Speed ◽  
Split Bregman ◽  
Reconstruction Image ◽  
Accelerate Convergence ◽  
Split Bregman Algorithm ◽  
Orthogonal Wavelet Transform

When original data is not complete or image degenerates, image reconstruction and recovery will be very important. In order to acquire reconstruction or recovery image with good quality, compressed sensing provides the possibility of achieving, and an image reconstruction algorithm based on compressed sensing with split Bregman method and fuzzy bases sparse representation is proposed, split strategy is applied in split Bregman algorithm in order to accelerate convergence speed; At the same time, discrete cosine transform and dual orthogonal wavelet transform are treated as bases to represent image sparsely, and image is reconstructed by using split Bregman algorithm. Experiments show that the proposed algorithm can improve convergence speed and reconstruction image quality.

Constructing totally interpolating wavelet frame systems

2015 ◽  
Vol 13 (03) ◽  
pp. 1550017
Author(s):  
Baobin Li
Keyword(s):  
Filter Banks ◽  
Scaling Function ◽  
Tight Frame ◽  
Special Structure ◽  
Dual Frame ◽  
Wavelet Frame ◽  
Continuous Linear ◽  
Wavelet Frames ◽  
Frame Systems ◽  
The Scaling Function

The system of totally interpolating wavelet frames is discussed in this paper, in which both the scaling function and one of wavelet functions are interpolating. It will be shown that corresponding filter banks possess the special structure, and the parametrization of filter banks is present. Moreover, we show that when considering tight frame systems with two generators, the Ron–Shen's continuous-linear-spline-based tight frame is the only one with totally interpolating property and symmetry. But in the dual frame context, more good examples of bi-frames with symmetric/antisymmetric property can be obtained and constructed, which in particular, include frames with the uniform symmetry.

scholarly journals OPTIMIZATION OF THE DEVELOPED OUTER SURFACE OF AN INDUSTRIAL OIL COOLER

2021 ◽  
Vol 2021 (4) ◽  
pp. 4764-4768
Author(s):  
ELENA SERGEEVNA BAYMETOVA ◽  
◽  
MARIA RAVILEVNA KOROLEVA ◽  
ALENA ALEKSEEVNA CHERNOVA ◽  
MICHAL KELEMEN ◽  
...  
Keyword(s):  
Heat Exchange ◽  
Numerical Experiment ◽  
Outer Surface ◽  
Optimization Problem ◽  
Heat Removal ◽  
Hydraulic Systems ◽  
Industrial Oil ◽  
Oil Cooler ◽  
Working Liquid

Heat removal from the working liquid of hydraulic systems requires the use of heat exchange devices - oil coolers with their geometry directly affecting their efficiency. This paper considers the issues of statement and implementation of the numerical experiment to solve the optimization problem for the industrial oil design.

scholarly journals Increasing Capacity of Intersections with Transit Priority

2016 ◽  
Vol 28 (6) ◽  
pp. 627-637 ◽  
Author(s):  
Yanxi Hao ◽  
Jing Teng ◽  
Yinsong Wang ◽  
Xiaoguang Yang
Keyword(s):  
Numerical Experiment ◽  
Optimization Problem ◽  
Low Cost ◽  
Linear Program ◽  
Signal Timing ◽  
Test Results ◽  
Transit Signal Priority ◽  
Proposed Model ◽  
Micro Simulation ◽  
Bus Lane

Dedicated bus lane (DBL) and transit signal priority (TSP) are two effective and low-cost ways of improving the reliability of transits. However, these strategies reduce the capacity of general traffic. This paper presents an integrated optimization (IO) model to improve the performance of intersections with dedicated bus lanes. The IO model integrated geometry layout, main-signal timing, pre-signal timing and transit priority. The optimization problem is formulated as a Mix-Integer-Non-Linear-Program (MINLP) that can be transformed into a Mix-Integer-Linear-Program (MILP) and then solved by the standard branch-and-bound technique. The applicability of the IO model is tested through numerical experiment under different intersection layouts and traffic demands. A VISSIM micro simulation model was developed and used to evaluate the performance of the proposed IO model. The test results indicate that the proposed model can increase the capacity and reduce the delay of general traffic when providing priority to buses.

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