Compressed Sampling of Spectrally Sparse Signals Using Sparse Circulant Matrices

Frequenz ◽  
2014 ◽  
Vol 68 (11-12) ◽  
Author(s):  
Guangjie Xu ◽  
Huali Wang ◽  
Lei Sun ◽  
Weijun Zeng ◽  
Qingguo Wang
Keyword(s):  
Circulant Matrices ◽  
Noise Robustness ◽  
Sparse Signals ◽  
Measurement Matrix ◽  
Compressed Sampling ◽  
Random Measurement ◽  
Compressive Performance ◽  
Generating Sequence ◽  
Periodic Autocorrelation ◽  
Selection Of

AbstractCirculant measurement matrices constructed by partial cyclically shifts of one generating sequence, are easier to be implemented in hardware than widely used random measurement matrices; however, the diminishment of randomness makes it more sensitive to signal noise. Selecting a deterministic sequence with optimal periodic autocorrelation property (PACP) as generating sequence, would enhance the noise robustness of circulant measurement matrix, but this kind of deterministic circulant matrices only exists in the fixed periodic length. Actually, the selection of generating sequence doesn't affect the compressive performance of circulant measurement matrix but the subspace energy in spectrally sparse signals. Sparse circulant matrices, whose generating sequence is a sparse sequence, could keep the energy balance of subspaces and have similar noise robustness to deterministic circulant matrices. In addition, sparse circulant matrices have no restriction on length and are more suitable for the compressed sampling of spectrally sparse signals at arbitrary dimensionality.

A Method of Seabed Soil Image Reconstruction Based on Compressed Sensing

2012 ◽  
Vol 487 ◽  
pp. 3-6
Author(s):  
Zhi Jing Xu ◽  
Li Jiang ◽  
Huan Lei Dai
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Random Projection ◽  
Experimental Result ◽  
Measurement Matrix ◽  
Image Block ◽  
Random Measurement ◽  
Low Dimensional ◽  
Seabed Soil ◽  
Selection Of

Compressed Sensing(CS) can project a high dimensional signal to a low dimensional signal by a random measurement matrix . As the projection calculation is time-consuming in the process of reconstruction, the reconstruction speed is greatly affected.In order to improve the reconstruction speed , some improvement in the selection of the measurement matrix and the design of the reconstruction algorithm is made. The wavelet transform is used to sparse decompose the image, and the very sparse random projection matrix is used as the measurement matrix, after the image block processing we use the OMP algorithm to reconstruct the image. The experimental result shows that this method could reduce the algorithm time and improved the reconstruction speed greatly.

scholarly journals Measurement Matrix Optimization via Mutual Coherence Minimization for Compressively Sensed Signals Reconstruction

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Ziran Wei ◽  
Jianlin Zhang ◽  
Zhiyong Xu ◽  
Yong Liu ◽  
Krzysztof Okarma
Keyword(s):  
Optimization Methods ◽  
Superior Performance ◽  
Gram Matrix ◽  
Sparse Signals ◽  
Two Dimensional ◽  
Measurement Matrix ◽  
Mutual Coherence ◽  
One Dimensional ◽  
Two Dimensional Image ◽  
Matrix Optimization

For signals reconstruction based on compressive sensing, to reconstruct signals of higher accuracy with lower compression rates, it is required that there is a smaller mutual coherence between the measurement matrix and the sparsifying matrix. Mutual coherence between the measurement matrix and sparsifying matrix can be expressed indirectly by the property of the Gram matrix. On the basis of the Gram matrix, a new optimization algorithm of acquiring a measurement matrix has been proposed in this paper. Firstly, a new mathematical model is designed and a new method of initializing measurement matrix is adopted to optimize the measurement matrix. Then, the loss function of the new algorithm model is solved by the gradient projection-based method of Gram matrix approximating an identity matrix. Finally, the optimized measurement matrix is generated by minimizing mutual coherence between measurement matrix and sparsifying matrix. Compared with the conventional measurement matrices and the traditional optimization methods, the proposed new algorithm effectively improves the performance of optimized measurement matrices in reconstructing one-dimensional sparse signals and two-dimensional image signals that are not sparse. The superior performance of the proposed method in this paper has been fully tested and verified by a large number of experiments.

scholarly journals A COMPARISON OF SIMILARITY MEASURES FOR CLUSTERING OF QRS COMPLEXES

2005 ◽  
Vol 17 (06) ◽  
pp. 324-331 ◽  
Author(s):  
KUANG-CHIUNG CHANG ◽  
CHENG WEN ◽  
MING-FENG YEH ◽  
REN-GUEY LEE
Keyword(s):  
Classification Accuracy ◽  
Clustering Algorithm ◽  
Similarity Measures ◽  
Threshold Value ◽  
Distance Measures ◽  
Noise Robustness ◽  
K Nearest Neighbor ◽  
Grey Relational Grade ◽  
Grey Relational ◽  
Selection Of

Similarity or distance measures play important role in the performance of algorithms for ECG clustering problems. This paper compares four similarity measures such as the city block (L1-norm), Euclidean (L2-norm), normalized correlation coefficient, and simplified grey relational grade for clustering of QRS complexes. Performances of the measures include classification accuracy, threshold value selection, noise robustness, execution time, and the capability of automated selection of templates. The clustering algorithm used is the so-called two-step unsupervised method. The best out of the 10 independent runs of the clustering algorithm with randomly selected initial template beat for each run is used to compare the performances of each similarity measure. To investigate the capability of automated selection of templates for ECG classification algorithms, we use the cluster centers generated by the clustering algorithm with various measures as templates. Four sets of templates are obtained, each set for a measure. And the four sets of templates are used in the k-nearest neighbor classification method to evaluate the performance of the templates. Tested with MIT/BIH arrhythmia data, we observe that the simplified grey relational grade outperforms the other measures in classification accuracy, threshold value selection, noise robustness, and the capability of automated selection of templates.

scholarly journals A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yao Wang ◽  
Jianjun Wang ◽  
Zongben Xu
Keyword(s):  
Sufficient Conditions ◽  
Tight Frame ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Tight Frames ◽  
Signal Recovery ◽  
Analysis Method ◽  
Measurement Matrix ◽  
Undersampled Data

This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frameD. By introducing the notion of blockD-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixedl2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms ofD. One of the main results of this note shows that if the measurement matrix satisfies the blockD-RIP with constantsδk<0.307, then the signals which are nearly blockk-sparse in terms ofDcan be stably recovered via mixedl2/l1-analysis in the presence of noise.

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