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• W4385446088 abstract "Conventional inversion of the discrete Fourier transform (DFT) requires all DFT coefficients to be known. When the DFT coefficients of a rasterized image (represented as a matrix) are known only within a pass band, the original matrix cannot be uniquely recovered. In many cases of practical importance, the matrix is binary and its elements can be reduced to either 0 or 1. This is the case, for example, for the commonly used QR codes. The a priori information that the matrix is binary can compensate for the missing high-frequency DFT coefficients and restore uniqueness of image recovery. This paper addresses, both theoretically and numerically, the problem of recovery of blurred images without any known structure whose high-frequency DFT coefficients have been irreversibly lost by utilizing the binarity constraint. We investigate theoretically the smallest band limit for which unique recovery of a generic binary matrix is still possible. Uniqueness results are proved for images of sizes , , and , where are prime numbers and an integer. Inversion algorithms are proposed for recovering the matrix from its band-limited (blurred) version. The algorithms combine integer linear programming methods with lattice basis reduction techniques and significantly outperform naive implementations. The algorithm efficiently and reliably reconstructs severely blurred binary matrices with only DFT coefficients." @default.
• W4385446088 created "2023-08-02" @default.
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• W4385446088 date "2023-08-01" @default.
• W4385446088 modified "2023-10-16" @default.
• W4385446088 title "Inversion of Band-Limited Discrete Fourier Transforms of Binary Images: Uniqueness and Algorithms" @default.
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• W4385446088 doi "https://doi.org/10.1137/22m1540442" @default.
• W4385446088 hasPublicationYear "2023" @default.
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