Study On Photonics-assisted Compressive Sensing

Compressive sensing is capable of capturing the wideband sparse signals with sub-Nyquist sampling rate,which reduces the pressure on the signal acquisition,storage and transmission.As the photonic devices have the advantages of large bandwidth,low loss and immunity to electromagnetic interference,combining these two technologies,photonics-assisted compressive sensing is a potential technique in signal processing.In this dissertation,the performance of existing photonics-assisted compressive sensing systems is analyzed,and at the same time,several novel photonics-assisted compressive sensing(hereinafter referred to as "photonic compressive sensing")schemes are proposed.First of all,a mathematical model is established for the photonic compressive sensing system based on spatial light modulator,and the limitation of this system is pointed out through theoretical analysis.Secondly,after studying the microwave photonic filter technique,we propose a compressive sensing scheme based on the method of microwave filter.After that,we establish a theoretical model to describe and analyze the compressive sensing scheme based on pulse stretch and compression.Meanwhile,a photonic compressive sensing system with spectral encoding is proposed,which not only achieves ultra-high-speed acquisition of wideband signals,but also simplifies the system structure and reduces the system cost.In addition,we combine the compressive sensing and the imaging technique to propose a single-pixel imaging system,which greatly reduces the pressure on data storage and processing in image signal acquisition.The major innovations and contributions of this dissertation are as follows.(1)Aimed at the scheme of photonic compressive sensing using spatial light modulator,a mathematical model is established using the frequency-to-time mapping theory to describe the mixing function realized in the frequency domain.Based on the far field condition,the minimum spectral bit duration of the random sequence and the upper limit of the random sequence length that can be applied in the spatial light modulator for mixing are pointed out,which should be taken into consideration in the system design.We also evaluate the signal recovery performance and perform simulations and experiments to verify the correctness of the theory.(2)A photonic compressive sensing scheme for analog-to-information conversion with a delay-line based microwave photonic filter is proposed,in order to achieve the low-pass filter function which is necessary and reduce the number of the wavelength of the optical carrier.In the first stage of low-pass filtering,the mixed signal is modulated on the multi-wavelength carrier and propagates through a dispersive element.In the second stage,the signal is split into multiple channels and passes through a set of tunable delay lines before being detected by the photodetectors and combined together.This system greatly reduces the number of tunable lasers.The two-stage mode provides more flexibility in the filter design and improves the performance of low-pass filtering in photonic compressive sensing schemes.(3)A photonics enabled compressive sensing scheme with spectral encoding using incoherent broadband source is proposed.The integration function is achieved in the time domain while the mixing function is realized via spectral encoding in the frequency domain.In the scheme,the programmable spectrum shaper is to slice and encode the spectrum of the broadband light.A dispersive element is employed to introduce group delay between adjacent wavelengths.Due to the correspondence between the group delays and the wavelengths,the input signal is multiplied with the random sequence and the mixed signal is integrated in the time domain.The scheme avoids the time-domain synchronization between repetitive pulses and random sequences,and has the advantage of tunable sampling rate and compression factor.Due to the use of incoherent broadband light source,the impacts of pulse envelope and non-ideal frequency-to-time mapping on the recovery performance are also avoided.(4)A single-pixel imaging system based on compressive sensing with spectral-domain optical mixing is proposed.The image information is recorded on the spectrum of the optical pulse and the mixing function with the random sequence is realized in the frequency domain.The pulse stretch,compression,modulation and synchronization in the time domain are avoided in comparison with these approaches based on photonic time stretch.The proposed scheme remarkably simplifies the system structure,and has the advantages of small size,low cost and low power consumption.We believe this scheme has a potential for the single-pixel imaging in the scenarios with a relatively low requirement on frame rate.In addition,based on the research of the microwave photonic filter,a design method of all-positive-coefficient microwave photonic filter with rectangular response is proposed.In the filter design,we obviate the need for negative coefficients by means of multiplying the impulse response sequence by a sequence alternating between +1 and-1 and adding a constant to the sequence.Regarding the filter implementation,we employ a broadband incoherent light source and a programmable spectrum shaper to generate required multiple wavelengths with appropriate intensities.Only one photodetector is used in the O/E conversion,making the system structurally and volumetrically advantageous.Based on the in-depth understanding of the mixing and integration function,a mathematical model is established to describe the measurement process in the photonic compressive sensing scheme based on pulse stretch and compression.We have proved that in each measurement process,sampling the peak value of the output pulse is equivalent to sampling the integration of the mixed product of the signal of interest and the pseudorandom sequence.Furthermore,we have analyzed the impact of the photodetector bandwidth on this equivalence and the signal recovery performance.Numerical results are presented to verify our theoretical findings.In conclusion,this dissertation focuses on the signal acquisition technique based on photonic compressive sensing.Due to the advantages of large bandwidth and immunity to electromagnetic interference offered by photonics,the presented research results are believed to be valuable in the acquisition of wideband time-domain signals and image signals.