Statistical compressive sensing method for Hadamard-based single-pixel microscopy supported by kernel density estimators

Hadamard-based single-pixel microscopy (HSPM) is a versatile non-conventional imaging technique where a binary function base is projected over the sample in a microscope setup to recover its information. One HSPM’s main challenge is the need to project numerous patterns to retrieve the image of the object under study. This leads to potential phototoxicity damage and a reduction in temporal resolution. Aiming to reduce the total pattern projection time, this study explores the use of statistical compressive sensing (CS) using the kernel density estimator (KDE) approach to learn the probability distribution of the most relevant Hadamard spectrum (HS) sampling coefficients, based on a large-scale dataset of 50,000 histopathology images. The probability distribution can then be sampled to generate the set of Hadamard patterns to be projected. The proposed KDE-guided CS method is implemented and tested on biological and nonbiological samples. An image resolution of 550 lp/mm was recovered at a 25% sampling ratio (SR) using the proposed method, a level not reached by the well-established TV-based approach. Moreover, compared to TV-based sampling, the Michelson contrast increased from 0.09 to 0.17 at a 25% SR and from 0.12 to 0.29 at a 30% SR. These results demonstrate the feasibility of the proposed method for HSPM CS applications.

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