Analytical Model for Photonic Compressive Sensing With Pulse Stretch and Compression

Abstract

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.

Principle and Recent Development in Photonic Time-Stretch Imaging

“…The recent development of PTS imaging systems are mainly in four categories: first, PTS imaging systems combined with shorter wavelength bands for better imaging resolutions and rich applications [68][69][70][71][72][73]; second, PTS imaging systems with faster speed [21,22,[26][27][28][29]57,58,74,79]; third, PTS imaging systems combined with data compression [11][12][13][14][15][16][17][18][75][76][77][78]; and the last, PTS imaging systems combined with deep learning for target classification [23][24][25]32,66].…”

“…Additionally, it can achieve a continuous ultrafast imaging speed of millions of frames per second, which is several magnitudes higher compared to traditional imaging techniques. Moreover, due to its inherent nature, it can combine other several recent optical technologies such as compressive sensing [10][11][12][13][14][15][16][17][18]22,29,75,76], nonlinear processing [76][77][78], amplification [4,79], and deep learning [80,81], which are beyond the capabilities of other imaging techniques.…”

A Compressed Sensing Recovery Algorithm Based on Support Set Selection

“…In the RD, a microwave signal is directly mixed with PRBS via a mixer and accumulated by an accumulator or a low-pass filter (LPF); this is done in awareness of the sampling rate being exponentially lower than the Nyquist rate, which was pioneering at that time. Recent years, researchers turned their eyes to photonics-enabled CS systems due to the advantages of low loss, large bandwidth, and high speed offered by photonics [13][14][15][16][17][18][19][20][21][22][23][24]. In [13], a CS system in a photonic link was demonstrated for the first time, which successfully recovered a 1 GHz harmonic signal with 500 MS/s sampling rate.…”

“…In [13], a CS system in a photonic link was demonstrated for the first time, which successfully recovered a 1 GHz harmonic signal with 500 MS/s sampling rate. Afterwards the researcher introduced the time stretch technique to broaden the pulse width in order to lower the sampling rate even further, and realized the integration process by compressing the optical pulses before photodiode (PD) [17,21,22]. Under this scheme, signals spanning from 900 MHz to 14.76 GHz can be recovered by a 500 MHz ADC.…”