Modified noiselet transform and its application to compressive sensing with optical single-pixel detectors

One of the main contributions of compressed sensing (CS) to optics is the introduction of single-pixel cameras (SPC). These imaging systems make use of structured aperture functions or structured illumination, which is usually based on Walsh-Hadamard functions or on orthogonal random matrices. An alternative approach, which is considered here, is based on discrete noiselets. The incoherence of noiselet functions with Haar wavelets is a strong argument for choosing them as the sensing basis. We have recently shown, how to modify the complex noiselet transform, in order to use it efficiently in SPC with binary spatial light modulators and how to compute the modified noiselet functions in bundles with a fast algorithm involving only integral additions and subtractions. Here we give a brief overview of the properties of the modified noiselet transform and present experimental results obtained with a SPC with the modified noiselet sensing matrices.