Single-pixel imaging: development and applications of adaptive methods

Single-pixel imaging is a recent paradigm that allows the acquisition of images at reasonably low cost by exploiting hardware compression of the data. The architecture of a single-pixel camera consists of only two elements: a spatial light modulator, and a single-point detector. The key idea is to measure the projection at the detector (i.e., the inner product) of the scene under view -the image- with some patterns. The post-processing of a sequence of measurements obtained with different patterns permits the restoring of the desired image. Single-pixel imaging has several advantages, which are of interest for different applications, and especially in the biomedical field. In particular, a time-resolved single-pixel imaging system benefits fluorescence lifetime sensing. Such a set-up can be coupled to a spectrometer, to supplement the lifetime with spectral information. However, the main limitation of single-pixel imaging is the speed of acquisition and/or image restoration, which is, as of today, not compatible with real-time applications. This thesis investigates fast acquisition/ restoration schemes for the targeting of biomedical applications using a single-pixel camera. First, a new acquisition strategy is reported, based on wavelet compression algorithms. This shows that these algorithms can significantly accelerate image recovery, compared to conventional schemes of the compressive sensing framework. Secondly, a novel technique is proposed to alleviate an experimental positivity constraint of the modulation patterns. With respect to the classical approaches, the proposed nonnegative matrix-factorization-based technique halves the number of patterns sent to the spatial light modulator, and hence halves the overall acquisition time. Finally, the applicability of these techniques is demonstrated for multispectral and/or time-resolved imaging, which are common modalities in biomedical imaging.