Iterative Filtered Correlation Imaging With Pseudo-inverse Compressed Sensing

Correlation imaging,as a new imaging method that has attracted much attention in recent years,is based on the second-order intensity correlation measurement of the light field to reconstruct the spatial information of the object.Compared with traditional imaging methods,correlated imaging technology has many significant advantages: the imaging resolution is high;the imaging can be carried out in a complex environment;the imaging can be carried out without a lens.However,at the same time,correlated imaging also faces the limitations of a large number of samples,complicated calculations,and low signal-to-noise ratio,which restrict the development of correlated imaging towards practicality.In recent years,as compressed sensing technology has gradually become popular,the combination of compressed sensing algorithm and associated imaging technology can better recover objects or signals under conditions far less than the Nyquist sampling limit.It is widely used in many fields such as magnetic resonance imaging,digital image and signal processing.This article is based on compressed sensing,aiming at the problem of low imaging signal-to-noise ratio,combining the pseudo-inverse with the compressed sensing algorithm and the correlation imaging technology,proposed pseudo-inverse compression correlation imaging.In the experiment of pseudo-inverse compression correlation imaging,we found that when the number of samples is the same,the signal-to-noise ratio of reconstructed image of pseudo-inverse compression correlation imaging is about 15 times higher than that of traditional compressed sensing correlation imaging.At the same time,the measurement matrix of pseudo-inverse compression correlation imaging is analyzed.Because the measurement matrix concentrates useful information on the diagonal and near the diagonal,the interference of noise on the reconstructed image is greatly reduced,and the quality of the reconstructed image is improved.This paper also introduces the iterative filtering method,and combines it with the pseudo-inverse compression associated imaging scheme,and proposes the pseudo-inverse compression associated imaging based on iterative filtering,the purpose is to reduce the number of samples while improving the signal-to-noise ratio.We use lowpass,bandpass,and highpass filtering methods to verify the universal applicability of pseudo-inverse compressed correlation imaging based on iterative filtering,the relationship between the number of samples and the signal-to-noise ratio of the three filtering methods in our scheme and the relationship between the number of iterations and the signal-to-noise ratio are also compared,and it is concluded that the application of the high-pass filtering method in our scheme has more advantages than the other two methods.we also found that the signal-to-noise ratio gradually increases as the number of iterations increases,which shows that the number of iterations also has an effect on the signal-to-noise ratio.And in the limited number of samples we use,the number of samples required for iterative filtered correlation imaging with pseudo-inverse compressed sensing is about 1/15 of the number of samples required for pseudo-inverse compression correlation imaging,which can be reduced to within0.1% of the Nyquist sampling limit.