Compressive Color Pattern Detection using Partial Orthogonal Circulant Sensing Matrix

Abstract : One key issue in compressive sensing is to design a sensing matrix that is random enough to have a good signal reconstruction quality and that also enjoys some desirable properties such that orthogonality or being circulant. The classic method to construct such sensing matrices is to first generate a full orthogonal circulant matrix and then select only a few rows. In this paper, we propose a refined construction of orthogonal circulant sensing matrices that generates a circulant matrix where only a given subset of its rows are orthogonal. That way, the generation method is a lot less constrained leading to better sensing matrices and we still have the desired properties. The proposed partial shift-orthogonal sensing matrix is compared to random and learned sensing matrices in the frame of signal reconstruction. This sensing matrix is pattern-dependent and thus efficient to detect color patterns and edges from the measurements of a color image.
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Submitted on : Wednesday, December 11, 2019 - 10:10:17 AM
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Sylvain Rousseau, David Helbert. Compressive Color Pattern Detection using Partial Orthogonal Circulant Sensing Matrix. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2020, 29 (7), pp.670-678. ⟨10.1109/TIP.2019.2927334⟩. ⟨hal-02166497⟩

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