Research On Single Pixel Imaging Based On Walsh Transform Measurement Matrix

As a new imaging technology,single pixel imaging has some unique imaging advantages compared with traditional imaging technology,such as high sensitivity,wide band response,high signal-to-noise ratio under weak light conditions,low cost and so on.The principle of single pixel imaging is mainly to modulate the light field by using the modulation structured light device,to receive the target signal by using a single pixel or a photodetector without resolution,and then to reconstruct the target image by using mathematical algorithm.At present,single pixel imaging has many potential applications in spectral imaging,microscopic imaging,three-dimensional imaging,biomedical imaging,information encryption and other fields.In recent years,researchers at home and abroad have carried out a large number of research work on single pixel imaging,and achieved fruitful results.However,in the process of promoting the application of single pixel imaging technology,the imaging quality and sampling efficiency are mainly restricted by each other.Under the same reconstruction algorithm,the quality of the reconstruction of the target object is directly determined by the merits of the system modulated light field.In the modulation process of single pixel imaging light field,it is necessary to prefabricate the measurement matrix,which generally includes two categories: random measurement matrix and deterministic measurement matrix.Among them,the random measurement matrix has good universality and is uniformly affected by noise,but its disadvantages are high computational complexity,large storage capacity and high uncertainty of reconstruction.The deterministic measurement matrix has good orthogonality and can reconstruct high quality target objects under full acquisition condition.It has low complexity and is easy to implement in hardware.The reconstruction performance is better than that of the random measurement matrix,but its universality is not good.In this paper,the advantages and disadvantages of the above two kinds of measurement matrix are comprehensively considered,and the optimization design of the new measurement matrix is mainly carried out.The main research contents are as follows:1.Starting from the Walsh function system,six different sequence Walsh transformation matrices are constructed respectively.According to the replication theory,these six Walsh transformation matrices are divided into three categories of different measurement matrices according to the sorting method and matrix structure: The ? class-Walsh transform(Walsh and Paley),the ? class-Walsh transform(Hadamard and C?Walsh),and the ? class-Walsh transform(Like?Walsh and X?Walsh).By comparing and analyzing the properties of the above measurement matrices and the image quality of single pixel,it is found that the image quality of ? class-Walsh transform is obviously better than the other two kinds of measurement matrices under the same conditions.2.Combining Walsh transformation matrix with Gold matrix,a new Walsh transformation pseudo-random measurement matrix is designed and constructed.The new measurement matrix has the advantages of both random measurement matrix and deterministic measurement matrix.A new deterministic measurement matrix is obtained by optimizing the Walsh transformation matrix by using biscubic interpolation method.The newly constructed measurement matrix not only maintains the original properties of Walsh transformation matrix,but also presents new characteristics because each matrix element value is transformed from integer to decimal.Further,the bicubic interpolation is performed on the pseudo-random measurement matrix of Walsh transform to obtain the pseudo-random measurement matrix of bicubic interpolation Walsh transform.The numerical simulation results show that the light field can achieve low sampling and high quality single pixel imaging after the modulation of the Walsh transform pseudorandom measurement matrix,bicubic interpolation Walsh transform measurement matrix and bicubic interpolation Walsh transform pseudorandom measurement matrix.3.A digital micromirror device(DMD)was used as a light field modulation device,and the single pixel imaging experiments of ? class Walsh(Walsh),? class Walsh(Hadamard)and ? class Walsh(Like?Walsh)measurement matrix were compared and analyzed.The results show that under the condition of low sampling,the reconstructed image quality of ? class Walsh transform(Walsh)measurement matrix is obviously better than that of the Column-Walsh transform and the Entropy class Walsh transform measurement matrix,and there is no double.Under the condition of full mining,the three kinds of measurement matrices can reconstruct the target image with high quality,which is consistent with the numerical simulation results.4.Using a digital light projector(DLP)as a light field modulation device,the image reconstruction performance of the new measurement matrix single pixel imaging constructed by bicubic interpolation method is verified experimentally.The results show that: Bicubic interpolation Walsh transformation pseudorandom measurement matrix can be used to achieve low sampling and high quality image reconstruction,and the image reconstruction quality of the target object is obviously better than the Bicubic interpolation Gold matrix and Bicubic interpolation Walsh matrix,which is consistent with the numerical simulation results.By adding glass film medium between the target object and the detector,the effectiveness of the new measurement matrix to improve the quality of single pixel imaging and the properties of single pixel imaging against scattering medium are further verified.