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Single-pixel imaging is an indirect imaging technique which utilizessimplified optical hardware and advanced computational methods. It offers novelsolutions for hyper-spectral imaging, polarimetric imaging, three-dimensionalimaging, holographic imaging, optical encryption and imaging through scatteringmedia. The main limitations for its use come from relatively high measurementand reconstruction times. In this paper we propose to reduce the requiredsignal acquisition time by using a novel sampling scheme based on a randomselection of Morlet wavelets convolved with white noise. While such functionsexhibit random properties, they are locally determined by Morlet waveletparameters. The proposed method is equivalent to random sampling of theproperly selected part of the feature space, which maps the measured imagesaccurately both in the spatial and spatial frequency domains. We compare bothnumerically and experimentally the image quality obtained with our samplingprotocol against widely-used sampling with Walsh-Hadamard or noiseletfunctions. The results show considerable improvement over the former methods,enabling single-pixel imaging at low compression rates on the order of a fewpercent.

Single-pixel imaging with Morlet wavelet correlated random patterns