Single-pixel imaging with sampling distributed over simplex vertices

Last week I posted a recently uploaded paper on using positive-only patterns in a single-pixel imaging system.

Today I just found another implementation looking for the same objective. This time the authors (from University of Warsaw, leaded by Rafał Kotyński) introduce the idea of simplexes, or how any point in some N-dimensional space can be located using only positive coordinates if you choose the correct coordinate system. Cool concept!

Fig.1 extracted from «Single-pixel imaging with sampling distributed over simplex vertices,»
Krzysztof M. Czajkowski, Anna Pastuszczak, and Rafał Kotyński, Opt. Lett. 44, 1241-1244 (2019)

Single-pixel imaging with sampling distributed over simplex vertices

by Krzysztof M. Czajkowski et al., on Optics Letters

Abstract:

We propose a method of reduction of experimental noise in single-pixel imaging by expressing the subsets of sampling patterns as linear combinations of vertices of a multidimensional regular simplex. This method also may be directly extended to complementary sampling. The modified measurement matrix contains nonnegative elements with patterns that may be directly displayed on intensity spatial light modulators. The measurement becomes theoretically independent of the ambient illumination, and in practice becomes more robust to the varying conditions of the experiment. We show how the optimal dimension of the simplex depends on the level of measurement noise. We present experimental results of single-pixel imaging using binarized sampling and real-time reconstruction with the Fourier domain regularized inversion method.

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