Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging
This addresses a computational efficiency challenge for researchers and engineers in compressed single-pixel imaging, though it is incremental as it builds on existing noiselet and Haar wavelet methods.
The paper tackled the problem of efficiently using complex-valued noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators, achieving the determination of m complex noiselet coefficients from m+1 binary sampling measurements and enabling real-time pattern generation through a modified transform.
Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally-efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.