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Image reconstruction based on circulant matrices

Carrasquinha, E; Amado, Conceição; Pires, Ana M.

Signal Processing: Image Communication, 63 (2018), 72-80

We propose a new method for image reconstruction based on circulant matrices. The novelty of this method is the image treatment using a simple and classical algebraic structure, the circulant matrix, which significantly reduces the computational effort, nevertheless providing reliable outputs. We compare the results with well established techniques such as the Principal Component Analysis (PCA) and the Discrete Fourier Transform (DFT), and the recently introduced Randomized Singular Value Decomposition (RSVD). We conclude that the quality is comparable whilst the computational time is considerably reduced.