Analytical Model for Photonic Compressive Sensing With Pulse Stretch and Compression

Compressive sensing (CS) with photonic technologies provides a promising way to acquire information with reduced measurement. Photonic CS with pulse stretch and compression has been proved to be capable of capturing wideband time-domain signals at extremely high equivalent sampling rate or images at high frame rate. In this approach, an input short pulse is first stretched by propagating through a dispersive medium and then the stretched pulse is modulated by a signal to be measured and a pseudorandom bit sequence (PRBS). The stretched pulse encoded with the signal and the PRBS is compressed in the time domain after passing a second dispersive medium with an opposite dispersion value. The time-domain compression of the stretched pulse was regarded as the integration function in the CS process (but it has never been proved), which is a key to realize time-domain downsampling or single-pixel imaging. In this paper, we fully investigate the theoretical framework of the photonic CS with optical pulse stretch and compression, and present an analytical model of the CS measurement matrix based on the analysis of the pulse stretch, modulation and compression, for the first time to our knowledge. Moreover, we prove the equivalence between the peak value of the compressed pulse and the integral value of the mixed signal, which is the basis of the analytical model. In addition, we further discuss the impact of the limited bandwidth of the employed photodetector on the measurement and the performance of signal reconstruction.