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Minimal mutual coherence of discrete noiselets and Haar wavelets makes thispair of bases an essential choice for the measurement and compression matricesin compressed-sensing-based single-pixel detectors. In this paper we propose anefficient way of using complex-valued and non-binary noiselet functions forobject sampling in single-pixel cameras with binary spatial light modulatorsand incoherent illumination. The proposed method allows to determine m complexnoiselet coefficients from m+1 binary sampling measurements. Further, weintroduce a modification to the complex fast noiselet transform, which enablescomputationally-efficient real-time generation of the binary noiselet-basedpatterns using efficient integer calculations on bundled patterns. The proposedmethod is verified experimentally with a single-pixel camera system using abinary spatial light modulator.

Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging