TY - GEN

T1 - Covariance matrix of a probability distribution for image dictionaries in compressed sensing

AU - Aida, Toshiaki

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number JP17K00340.

PY - 2018/12/10

Y1 - 2018/12/10

N2 - Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.

AB - Sparse representation is one of the principles for the most effective signal processing, and makes it possible for us to infer from less data. The framework of signal processing based on it is called compressed sensing or compressive sensing, where dictionary matrices play an essential role of the basis for sparse representation. In our previous work, we successfully derived an analytical expression of the probability distribution followed by image dictionaries for the images generated by the Gaussian model [1]. However, we have found that the distribution has a difficulty of a divergent covariance matrix, which is needed for an analytical performance evaluation of image processing by compressed sensing. Therefore, it is the purpose of this paper to solve the difficulty and to open the way to the evaluation.

KW - Compressed sensing

KW - Covariance matrix

KW - Dictionary matrix

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M3 - Conference contribution

AN - SCOPUS:85060444593

T3 - International Conference on Control, Automation and Systems

SP - 829

EP - 832

BT - International Conference on Control, Automation and Systems

PB - IEEE Computer Society

T2 - 18th International Conference on Control, Automation and Systems, ICCAS 2018

Y2 - 17 October 2018 through 20 October 2018

ER -