scholarly journals Column normalization of a random measurement matrix

2018 ◽  
Vol 23 ◽  
Author(s):  
Shahar Mendelson
Keyword(s):  
Measurement Matrix ◽  
Random Measurement

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 Universal Measurement Matrix Design for Sparse and Co-Sparse Signal Recovery

2021 ◽  
Vol 12 (6) ◽  
pp. 404-411
Author(s):  
Sudha Hanumanthu Et.al
Keyword(s):  
Recovery Time ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Measurement Matrix ◽  
Mutual Coherence ◽  
Memory Space ◽  
Random Measurement ◽  
Hardware Realization ◽  
Recovery Error ◽  
Matrix Design

Compressed Sensing (CS) avails mutual coherence metric to choose the measurement matrix that is incoherent with dictionary matrix. Random measurement matrices are incoherent with any dictionary, but their highly uncertain elements necessitate large storage and make hardware realization difficult. In this paper deterministic matrices are employed which greatly reduce memory space and computational complexity. To avoid the randomness completely, deterministic sub-sampling is done by choosing rows deterministically rather than randomly, so that matrix can be regenerated during reconstruction without storing it. Also matrices are generated by orthonormalization, which makes them highly incoherent with any dictionary basis. Random matrices like Gaussian, Bernoulli, semi-deterministic matrices like Toeplitz, Circulant and full-deterministic matrices like DFT, DCT, FZC-Circulant are compared. DFT matrix is found to be effective in terms of recovery error and recovery time for all the cases of signal sparsity and is applicable for signals that are sparse in any basis, hence universal.

A Note on Stability and Instance Optimality in Compressed Sensing

2011 ◽  
Vol 130-134 ◽  
pp. 4194-4197
Author(s):  
Sheng Zhang ◽  
Pei Xin Ye
Keyword(s):  
Compressed Sensing ◽  
Noisy Data ◽  
Sparse Signal ◽  
Measurement Matrix ◽  
Random Measurement ◽  
Restricted Isometry Constant ◽  
Instance Optimality ◽  
Measurement Vector ◽  
The Stability ◽  
Signal Vector

In this note, it is proved that every -sparse signal vector can be recovered stably from the measurement vector via minimization as soon as the restricted isometry constant of the measurement matrix is smaller than . Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Also we obtain the results on the stability and instance optimality for some random measurement matrices.

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