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Compressed Sensing for Phase Unwrapping of Interferometric SAR Data
Toshiaki Aida 제어로봇시스템학회 2017 제어로봇시스템학회 국제학술대회 논문집 Vol.2017 No.10
We approach to the problem of wave-front reconstruction via phase unwrapping of interferograms observed by interferometric synthetic aperture radar (SAR), from the viewpoints of Bayesian statistical inference and compressed sensing. For this purpose, we apply sparse representation for compressed sensing to the Bayesian wave-front reconstruction model from SAR interferograms by Saika and Uezu [1]. In the formulation of the problem taking sparse representation into account, the MAP estimate is found to lead to a phase unwrapping algorithm which can be interpreted as a quadratic programming problem. Numerical experiments on an artificial wave-front make it clear that the algorithm effectively removes noise to reconstruct the wave-front, although it suffers from the errors similar to block noise in image processing.
Covariance Matrix of a Probability Distribution for Image Dictionaries in Compressed Sensing
Toshiaki Aida 제어로봇시스템학회 2018 제어로봇시스템학회 국제학술대회 논문집 Vol.2018 No.10
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.
Probability Distribution of an Image Dictionary for Compressed Sensing
Yuhei Ashida,Toshiaki Aida 제어로봇시스템학회 2016 제어로봇시스템학회 국제학술대회 논문집 Vol.2016 No.10
Compressed sensing is one of the most effective signal processing methods through the sparse representation of inferred data, in which dictionary matrices play an essential role and they are learned by feature extraction methods such as K-SVD ones. Therefore, in general, it requires a considerable amount of computational cost to construct a dictionary matrix. In this paper, we analytically derive the expression of the probability distribution followed by an image dictionary for compressed sensing, assuming that grey scale images are generated by the Gaussian model. This result enables us to directly generate a dictionary matrix for images with no edge, and can be the first step to analytical performance evaluation of image processing by compressed sensing.
Sparse Representation Approach to Inverse Halftoning in Terms of DCT Dictionary
Yuhri Ohta,Toshiaki Aida 제어로봇시스템학회 2014 제어로봇시스템학회 국제학술대회 논문집 Vol.2014 No.10
The problem of inverse halftoning is approached on the basis of compressed sensing, which enables us to make significantly efficient inference through the sparse representation of data to be inferred. For this purpose, we have adopted a DCT dictionary as a basis to represent image patches. In the Bayesian formulation of the problem taking the sparse representation into account, the MAP estimate is found to lead to an inverse halftoning algorithm which can be interpreted as a linear programming problem. Numerical simulations have successfully confirmed the effectiveness of the algorithm, which allows us to conclude that the compressed sensing approach is efficient to the problem of inverse halftoning.
Sparse Representation Approach to Inverse Halftoning by Means of K-SVD Dictionary
Masahiro Hirao,Toshiaki Aida 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10
We approach to the problem of inverse halftoning within the frameworks of Bayesian inference and compressed sensing, which is one of the most effective signal processing methods through sparse representation. In this paper, we adopt the K-SVD dictionary for the sparse representation of an original image to be inferred, and develop our previous work with the DCT dictionary restricted to a small number of the slowest basis vectors. The K-SVD dictionary is known to have higher efficiency for sparse representation than the DCT one. Therefore, we can expect that it helps us overcome a heavily ill-posed property of the problem. Numerical analysis confirms the effectiveness of our approach with the K-SVD dictionary, and makes clear the difference between the characteristics of the K-SVD dictionary and those of the restricted DCT one.