Research On Ghost Imaging Reconstruction Based On Multidimensional Walsh Transform

Ghost imaging,as a new optical imaging technology rising in recent 20 years,is totally different from the traditional optical imaging principle,and has its unique imaging advantages,such as: it can image the target in the harsh or complex optical environment;it can break through the classical Rayleigh diffraction limit to achieve high-resolution imaging and so on.In the traditional ghost imaging scheme,the random patterns are usually used as the illumination patterns,and the number of samples is dozens of times of the number of image pixels to achieve good imaging results.Recently,it has been found that high quality imaging results can be obtained by using Hadamard and other orthogonal basis patterns instead of random patterns.What's impressive is that one-dimensional Hadamard transform ghost imaging can quickly achieve near perfect imaging effect.But the disadvantage of this scheme is that it can't get good imaging effect when under sampling.As we all know,compared with one-dimensional transform,two-dimensional Walsh transform has the advantages of simple calculation and strong energy concentration.But the problem is that the representation of two-dimensional Walsh transform by twice matrix multiplication can't fit the existing ghost imaging system of one-dimensional transform.In this paper,it is found that the one-dimensional sampling process of obtaining the bucket detection matrix by using the "most natural" Walsh basis patterns as the illumination patterns is mathematically equivalent to the two-dimensional transform,and then the two-dimensional Walsh transform of the detection matrix can obtain perfect imaging results in principle.Numerical simulations and experimental results show that two-dimensional Walsh transform ghost imaging can use less coefficients to reconstruct sharp images;the time complexity and the maximum storage space of the scheme are exponentially reduced,thus significantly reducing thereconstruction time.After that,this paper proposes a four-dimensional Walsh transform ghost imaging theoretical model by combining multidimensional vector matrix theory with ghost imaging system.In this scheme,the four-dimensional Walsh matrix is used as the measurement matrix,and the process of sampling and reconstruction is equivalent to the four-dimensional Walsh transform.The energy of the image is focused on the upper left corner by using the four-dimensional Walsh transform.We reorder the four-dimensional Walsh patterns according to zigzag scanning mode,which can achieve the priority sampling of key coefficients.Numerical simulation and experimental results show that the method can produce clear reconstructed image when the sampling rate is 20%.The main work of this paper is to make use of the energy concentration characteristics of multidimensional Walsh transform,and to provide the possibility of minimizing the number of samples without prior knowledge of the target object.To a certain extent,this scheme solves the problem of poor imaging quality of traditional one-dimensional Hadamard transform imaging at low sampling rate,and has more application space in real-time imaging and other fields.