An AK-BRP dictionary learning algorithm for video frame sparse representation in compressed sensing

2016 ◽  
Vol 76 (22) ◽  
pp. 23739-23755
Author(s):  
Yang Qian ◽  
Lei Li ◽  
Zhenzhen Yang ◽  
Feifei Zhou
Keyword(s):  
Compressed Sensing ◽  
Sparse Representation ◽  
Dictionary Learning ◽  
Learning Algorithm ◽  
Video Frame

scholarly journals Analysis Sparse Representation for Nonnegative Signals Based on Determinant Measure by DC Programming

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yujie Li ◽  
Benying Tan ◽  
Atsunori Kanemura ◽  
Shuxue Ding ◽  
Wuhui Chen
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Optimization Problem ◽  
Learning Algorithm ◽  
State Of The Art ◽  
Optimization Methods ◽  
Dc Programming ◽  
Sparse Model ◽  
Alternative Approach ◽  
Difference Of Convex

Analysis sparse representation has recently emerged as an alternative approach to the synthesis sparse model. Most existing algorithms typically employ the l0-norm, which is generally NP-hard. Other existing algorithms employ the l1-norm to relax the l0-norm, which sometimes cannot promote adequate sparsity. Most of these existing algorithms focus on general signals and are not suitable for nonnegative signals. However, many signals are necessarily nonnegative such as spectral data. In this paper, we present a novel and efficient analysis dictionary learning algorithm for nonnegative signals with the determinant-type sparsity measure which is convex and differentiable. The analysis sparse representation can be cast in three subproblems, sparse coding, dictionary update, and signal update, because the determinant-type sparsity measure would result in a complex nonconvex optimization problem, which cannot be easily solved by standard convex optimization methods. Therefore, in the proposed algorithms, we use a difference of convex (DC) programming scheme for solving the nonconvex problem. According to our theoretical analysis and simulation study, the main advantage of the proposed algorithm is its greater dictionary learning efficiency, particularly compared with state-of-the-art algorithms. In addition, our proposed algorithm performs well in image denoising.

Sparse angle CT reconstruction with weighted dictionary learning algorithm based on adaptive group-sparsity regularization

2021 ◽  
pp. 1-18
Author(s):  
Tiejun Yang ◽  
Lu Tang ◽  
Qi Tang ◽  
Lei Li
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Learning Algorithm ◽  
Basic Unit ◽  
Ct Reconstruction ◽  
Group Sparsity ◽  
Sparsity Regularization ◽  
Smoothing Effects ◽  
Structural Details ◽  
Non Local

OBJECTIVE: In order to solve the blurred structural details and over-smoothing effects in sparse representation dictionary learning reconstruction algorithm, this study aims to test sparse angle CT reconstruction with weighted dictionary learning algorithm based on adaptive Group-Sparsity Regularization (AGSR-SART). METHODS: First, a new similarity measure is defined in which Covariance is introduced into Euclidean distance, Non-local image patches are adaptively divided into groups of different sizes as the basic unit of sparse representation. Second, the weight factor of the regular constraint terms is designed through the residuals represented by the dictionary, so that the algorithm takes different smoothing effects on different regions of the image during the iterative process. The sparse reconstructed image is modified according to the difference between the estimated value and the intermediate image. Last, The SBI (Split Bregman Iteration) iterative algorithm is used to solve the objective function. An abdominal image, a pelvic image and a thoracic image are employed to evaluate performance of the proposed method. RESULTS: In terms of quantitative evaluations, experimental results show that new algorithm yields PSNR of 48.20, the maximum SSIM of 99.06% and the minimum MAE of 0.0028. CONCLUSIONS: This study demonstrates that new algorithm can better preserve structural details in reconstructed CT images. It eliminates the effect of excessive smoothing in sparse angle reconstruction, enhances the sparseness and non-local self-similarity of the image, and thus it is superior to several existing reconstruction algorithms.

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Geophysics ◽  
2021 ◽  
pp. 1-52
Author(s):  
Nanying Lan ◽  
Zhang Fanchang ◽  
Chuanhui Li
Keyword(s):  
Compressed Sensing ◽  
Dictionary Learning ◽  
Seismic Data ◽  
Learning Algorithm ◽  
Interpolation Method ◽  
Superior Performance ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Data Interpolation ◽  
Interpolation Model

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image under-ground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or under-sampled data. Under the framework of compressed sensing, we propose a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the Elastic-Net, we first develop the elastic half norm regularization as a sparsity constraint, and establish a robust high-dimensional interpolation model with this technique. Then, considering the multi-dimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that, this method has superior performance and higher computational efficiency in both noise-free and noisy seismic data interpolation, compared to extensively utilized dictionary learning-based interpolation methods.

scholarly journals Attenuating seismic noise via incoherent dictionary learning

2018 ◽  
Vol 15 (4) ◽  
pp. 1327-1338
Author(s):  
Juan Wu ◽  
Min Bai
Keyword(s):  
Sparse Representation ◽  
Image Denoising ◽  
Dictionary Learning ◽  
Seismic Data ◽  
Learning Algorithm ◽  
Random Noise ◽  
Learning Technology ◽  
Image Patches ◽  
Seismic Images ◽  
Traditional Image

Abstract We propose to apply an incoherent dictionary learning algorithm for reducing random noise in seismic data. The image denoising algorithm based on incoherent dictionary learning is proposed for solving the problem of losing partial texture information using traditional image denoising methods. The noisy image is firstly divided into different image patches, and those patches are extracted for dictionary learning. Then, we introduce the incoherent dictionary learning technology to update the dictionary. Finally, sparse representation problem is solved to obtain sparse representation coefficients by sparse coding algorithm. The denoised data can be obtained by reconstructing the image using the sparse coefficients. Application of the incoherent dictionary learning method to seismic images presents successful performance and demonstrates its superiority to the state-of-the-art denoising methods.

Ultrasonic Block Compressed Sensing Imaging Reconstruction Algorithm Based on Wavelet Sparse Representation

2020 ◽  
Vol 16 (3) ◽  
pp. 262-272
Author(s):  
Guangzhi Dai ◽  
Zhiyong He ◽  
Hongwei Sun
Keyword(s):  
Compressed Sensing ◽  
Sparse Representation ◽  
Linear Array ◽  
Imaging System ◽  
Ultrasonic Imaging ◽  
Large Data ◽  
Reconstruction Algorithm ◽  
Array Transducer ◽  
Total Data ◽  
Block Compressed Sensing

Background: This study is carried out targeting the problem of slow response time and performance degradation of imaging system caused by large data of medical ultrasonic imaging. In view of the advantages of CS, it is applied to medical ultrasonic imaging to solve the above problems. Objective: Under the condition of satisfying the speed of ultrasound imaging, the quality of imaging can be further improved to provide the basis for accurate medical diagnosis. Methods: According to CS theory and the characteristics of the array ultrasonic imaging system, block compressed sensing ultrasonic imaging algorithm is proposed based on wavelet sparse representation. Results: Three kinds of observation matrices have been designed on the basis of the proposed algorithm, which can be selected to reduce the number of the linear array channels and the complexity of the ultrasonic imaging system to some extent. Conclusion: The corresponding simulation program is designed, and the result shows that this algorithm can greatly reduce the total data amount required by imaging and the number of data channels required for linear array transducer to receive data. The imaging effect has been greatly improved compared with that of the spatial frequency domain sparse algorithm.

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