scholarly journals Efficient Implementations for Orthogonal Matching Pursuit

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1507
Author(s):  
Hufei Zhu ◽  
Wen Chen ◽  
Yanpeng Wu
Keyword(s):  
Computational Complexity ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Cholesky Factorization ◽  
Gram Matrix ◽  
Numerical Errors ◽  
Almost All ◽  
Matrix Vector ◽  
Better Than

Based on the efficient inverse Cholesky factorization, we propose an implementation of OMP (called as version 0, i.e., v0) and its four memory-saving versions (i.e., the proposed v1, v2, v3 and v4). In the simulations, the proposed five versions and the existing OMP implementations have nearly the same numerical errors. Among all the OMP implementations, the proposed v0 needs the least computational complexity, and is the fastest in the simulations for almost all problem sizes. As a tradeoff between computational complexities/time and memory requirements, the proposed v1 seems to be better than all the existing ones when only considering the efficient OMP implementations storing G (i.e., the Gram matrix of the dictionary), the proposed v2 and v3 seem to be better than the only existing one when only considering the efficient implementations not storing G, and the proposed v4 seems to be better than the naive implementation that has the (known) minimum memory requirements. Moreover, all the proposed five versions only include parallelizable matrix-vector products in each iteration, and do not need any back-substitutions that are necessary in some existing efficient implementations (e.g., those utilizing the Cholesky factorization).

scholarly journals Endmember Learning with K-Means through SCD Model in Hyperspectral Scene Reconstructions

2019 ◽  
Vol 5 (11) ◽  
pp. 85 ◽  
Author(s):  
Ayan Chatterjee ◽  
Peter W. T. Yuen
Keyword(s):  
Dictionary Learning ◽  
Sparse Coding ◽  
Clustering Algorithm ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Scene Reconstruction ◽  
Data Sets ◽  
Practical Applications ◽  
Input Dataset ◽  
Better Than

This paper proposes a simple yet effective method for improving the efficiency of sparse coding dictionary learning (DL) with an implication of enhancing the ultimate usefulness of compressive sensing (CS) technology for practical applications, such as in hyperspectral imaging (HSI) scene reconstruction. CS is the technique which allows sparse signals to be decomposed into a sparse representation “a” of a dictionary D u . The goodness of the learnt dictionary has direct impacts on the quality of the end results, e.g., in the HSI scene reconstructions. This paper proposes the construction of a concise and comprehensive dictionary by using the cluster centres of the input dataset, and then a greedy approach is adopted to learn all elements within this dictionary. The proposed method consists of an unsupervised clustering algorithm (K-Means), and it is then coupled with an advanced sparse coding dictionary (SCD) method such as the basis pursuit algorithm (orthogonal matching pursuit, OMP) for the dictionary learning. The effectiveness of the proposed K-Means Sparse Coding Dictionary (KMSCD) is illustrated through the reconstructions of several publicly available HSI scenes. The results have shown that the proposed KMSCD achieves ~40% greater accuracy, 5 times faster convergence and is twice as robust as that of the classic Spare Coding Dictionary (C-SCD) method that adopts random sampling of data for the dictionary learning. Over the five data sets that have been employed in this study, it is seen that the proposed KMSCD is capable of reconstructing these scenes with mean accuracies of approximately 20–500% better than all competing algorithms adopted in this work. Furthermore, the reconstruction efficiency of trace materials in the scene has been assessed: it is shown that the KMSCD is capable of recovering ~12% better than that of the C-SCD. These results suggest that the proposed DL using a simple clustering method for the construction of the dictionary has been shown to enhance the scene reconstruction substantially. When the proposed KMSCD is incorporated with the Fast non-negative orthogonal matching pursuit (FNNOMP) to constrain the maximum number of materials to coexist in a pixel to four, experiments have shown that it achieves approximately ten times better than that constrained by using the widely employed TMM algorithm. This may suggest that the proposed DL method using KMSCD and together with the FNNOMP will be more suitable to be the material allocation module of HSI scene simulators like the CameoSim package.

Quantitative analysis of static equilibrium in women after mastectomy

2014 ◽  
Vol 14 (1) ◽  
pp. 81-87
Author(s):  
Maciej Rachwał ◽  
Justyna Drzał-Grabiec ◽  
Katarzyna Walicka-Cupryś ◽  
Aleksandra Truszczyńska
Keyword(s):  
Mean Amplitude ◽  
Control Group ◽  
Foot Pressure ◽  
Locomotor System ◽  
Center Of Foot Pressure ◽  
The Mean ◽  
Almost All ◽  
Posture Stability ◽  
Mastectomy Group ◽  
Better Than

Abstract Background: The post-mastectomy changes to the locomotor system are related to the scar and adhesion or to the lymphatic edema after amputation which, in turn, lead to local and global distraction of the work of the muscles. These changes lead to body statics disturbance that changes the projection of the center of gravity and worsens motor response due to changing of the muscle sensitivity. Objective: The aim of the study was to evaluate the static balance of women after undergoing mastectomy. Methods: The study included 150 women, including 75 who underwent mastectomy (mean age: 60±7.6) years, mean body mass index (BMI): 26 (±3.6) kg/m2) and 75 who were placed in the control group with matched age and BMI. The study was conducted using a tensometric platform. Results: Statistically significant differences were found for almost all parameters between the post-mastectomy group and group of healthy women, regarding center of foot pressure (COP) path length in the Y and X axes and the mean amplitude of COP. Conclusions: First, the findings revealed that balance in post-mastectomy women is significantly better than in the control group. Second, physiotherapeutic treatment of post-mastectomy women may have improved their posture stability compared with their peers.

scholarly journals Simultaneous Seismic Sources Separation Based on Matrioshka Orthogonal Matching Pursuit, Application in Oil and Gas Exploration

2020 ◽  
Vol 58 (7) ◽  
pp. 4529-4546
Author(s):  
Ekaterina Shipilova ◽  
Michel Barret ◽  
Matthieu Bloch ◽  
Jean-Luc Boelle ◽  
Jean-Luc Collette
Keyword(s):  
Oil And Gas ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Seismic Sources ◽  
Oil And Gas Exploration

Design and Generalization Analysis of Orthogonal Matching Pursuit Algorithms

2011 ◽  
Vol 57 (8) ◽  
pp. 5326-5341 ◽  
Author(s):  
Zakria Hussain ◽  
John Shawe-Taylor ◽  
David R. Hardoon ◽  
Charanpal Dhanjal
Keyword(s):  
Matching Pursuit ◽  
Orthogonal Matching Pursuit
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