scholarly journals Feasibility Pump Algorithm for Sparse Representation under Gaussian Noise

Algorithms ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 88
Author(s):  
Florin Ilarion Miertoiu ◽  
Bogdan Dumitrescu
Keyword(s):  
Gaussian Noise ◽  
Regularization Parameter ◽  
Matching Pursuit ◽  
Representation Error ◽  
Iterative Shrinkage ◽  
Support Size ◽  
Feasibility Pump ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding ◽  
Better Than

In this paper, the Feasibility Pump is adapted for the problem of sparse representations of signals affected by Gaussian noise. This adaptation is tested and then compared to Orthogonal Matching Pursuit (OMP) and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The feasibility pump recovers the true support much better than the other two algorithms and, as the SNR decreases and the support size increases, it has a smaller recovery and representation error when compared with its competitors. It is observed that, in order for the algorithm to be efficient, a regularization parameter and a weight term for the error are needed.

An Adaptive Regularized Fast Iterative Shrinkage-Thresholding Algorithm for Image Reconstruction in Compressed Sensing

2013 ◽  
Vol 710 ◽  
pp. 593-597
Author(s):  
Xin Meng ◽  
Shi Fang Duan ◽  
She Xiang Ma
Keyword(s):  
Image Quality ◽  
Compressed Sensing ◽  
Objective Function ◽  
Time Complexity ◽  
Regularization Parameter ◽  
Iteration Process ◽  
Reconstructed Image ◽  
Iterative Shrinkage ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

Aiming at the problems of worse reconstructed image quality and larger time complexity of the fast iterative shrinkage-thresholding algorithm in compressed sensing, this paper presents adaptive regularized fast iterative shrinkage-thresholding algorithm. This algorithm brings in the idea of adaptively selecting regularization parameter on the basis of using gradient method and threshold shrinkage to minimize the objective function. During the iteration process regularization parameter is adaptively selected from the whole value in order to adjust the proportion of the former part and the latter part of the objective function value. Simulation results show that the proposed algorithm, compared with the traditional algorithms, obtains the better reconstructed image quality and lower time complexity.

scholarly journals Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Ruirui Kang ◽  
Gangrong Qu ◽  
Bin Cao ◽  
Long Yan
Keyword(s):  
Compressive Sensing ◽  
Acquisition Time ◽  
Reference Image ◽  
Mr Images ◽  
Mr Image ◽  
Iterative Shrinkage ◽  
Novel Method ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding ◽  
Better Than

It is challenging to save acquisition time and reconstruct a medical magnetic resonance (MR) image with important details and features from its compressive measurements. In this paper, a novel method is proposed for longitudinal compressive sensing (LCS) MR imaging (MRI), where the similarity between reference and acquired image is combined with joint sparsifying transform. Furthermore, the joint sparsifying transform with the wavelet and the Contourlet can efficiently represent both isotropic and anisotropic features and the objective function is solved by extended smooth-based monotone version of the fast iterative shrinkage thresholding algorithm (SFISTA). The experiment results demonstrate that the existing regularization model obtains better performance with less acquisition time and recovers both edges and fine details of MR images, much better than the existing regularization model based on the similarity and the wavelet transform for LCS-MRI.

Accelerated 3D blind separation of convolved mixtures based on the fast iterative shrinkage thresholding algorithm for adaptive multiple subtraction

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. V99-V113 ◽  
Author(s):  
Zhong-Xiao Li ◽  
Zhen-Chun Li
Keyword(s):  
Field Data ◽  
Optimization Problem ◽  
Computational Cost ◽  
Computation Time ◽  
Blind Separation ◽  
L1 Norm ◽  
Norm Minimization ◽  
Iterative Shrinkage ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

scholarly journals Fast Algorithms for the Anisotropic LLT Model in Image Denoising

2011 ◽  
Vol 1 (3) ◽  
pp. 264-283 ◽  
Author(s):  
Zhi-Feng Pang ◽  
Li-Lian Wang ◽  
Yu-Fei Yang
Keyword(s):  
Convergence Rate ◽  
Image Denoising ◽  
Projection Method ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Minimization Problems ◽  
Iterative Shrinkage ◽  
Speed Up ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

AbstractIn this paper, we propose a new projection method for solving a general minimization problems with twoL1-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rateO(k−2). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.

scholarly journals A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3074 ◽  
Author(s):  
Shulin Pan ◽  
Ke Yan ◽  
Haiqiang Lan ◽  
José Badal ◽  
Ziyu Qin
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Seismic Data ◽  
Real Data ◽  
Training Dataset ◽  
Reflection Coefficients ◽  
Deconvolution Algorithm ◽  
Iterative Shrinkage ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

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.

Sign in / Sign up

Export Citation Format

Share Document