Compressed Sensing, ASBSR-method of image sampling and reconstruction and the problem of digital image acquisition with the lowest possible sampling rate
| Autor: | Yaroslavsky, Leonid P. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Compressed Sensing: Methods, Theory and Applications, Chapt.1., Ed. Jonathon M. Sheppard, Nova Publishers, 2018 |
| Druh dokumentu: | Working Paper |
| Popis: | The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling rate sufficient for signal reconstruction with a given accuracy is equal to the spectrum sparsity of the signal sparse approximation that has this accuracy. It is revealed that the compressed sensing approach, which was advanced as a solution to the sampling rate minimization problem, is far from reaching the sampling rate theoretical minimum. Potentials and limitations of compressed sensing are demystified using a simple and intutive model, A method of image Arbitrary Sampling and Bounded Spectrum Reconstruction (ASBSR-method) is described that allows to draw near the image sampling rate theoretical minimum. Presented and discussed are also results of experimental verification of the ASBSR-method and its possible applicability extensions to solving various underdetermined inverse problems such as color image demosaicing, image in-painting, image reconstruction from their sparsely sampled or decimated projections, image reconstruction from the modulus of its Fourier spectrum, and image reconstruction from its sparse samples in Fourier domain Comment: 28 pages, 19 figures |
| Databáze: | arXiv |
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