Compressive sensing and its potential for infrared applications

Compressive sensing (CS) allows the reconstruction of signals acquired at sampling frequency below the Nyquist rate relying on the assumption that the acquired signal is sparse (i.e it exhibits a certain degree of correlation). The possibility of undersampling a signal without losing significant information is accomplished by means of a specific integral transformation. For radiometric and spectroscopic signals, this transformation is performed by an optical subsystem spatially modulating the light and by a single pixel detector. Due to these characteristics CS can lead to the development of devices characterized by a reduction in terms of mass, volume and memory budgets. CS theory can be applied to a wide range of optical instruments. After a brief theoretical background, the paper will describe some promising CS applications in the infrared spectral range.