Research On Image Reconruction Technique Based On Convolution Fractional Transforms

Image reconstruction technique is a kind of important data synthesis and information processing method in measurement and imaging system.To obtain a high-quality image,a transmission model of object data is needed to be made according to experimental system.The data processing algorithm is also required for this application.The model has to be improved properly,to receive a result being much closed to true system.For instance,deep learning can be used to finish this task by training a lot of prior information.It is a difficult that to get a high accurate output with image reconstruction method.A vital reason is that the measured data is insufficient.At the same time,linear and time-invariant information processing systems can be regarded as a convolution,which has input signal and attribute function of the system.To express the discrete format of the convolution model,this thesis is focused on imaging system and gives the concept of fractional convolution-based transform(FCBT).The proposed transform is also embedded into matching pursuit algorithm(MPA)and iterative algorithm with multiple intensity images for image reconstruction.The main research works are listed as follows.A fractional-order transform having a changeable form is proposed by studying the transform integral definition of fractional Fourier transform and Gyrator transform.The new transform is named as FCBT.This transform includes two variational different phase function except the order.A discrete algorithm of FCBT is determined for the application of discrete signal and image processing.To achieve fast computation task,fast Fourier transform(FFT)is applied for designing the algorithm of the transform.The fast algorithm is matched with large volume of data for real-time calculation.The discrete algorithm is employed for the simple application of signal and image processing,such as frequency doubling and signal reconstruction.FCBT is also compared with fractional Fourier transform and Gyrator at the aspects of properties and application feature.Compression sensing technique based on FCBT,is introduced into sparse image reconstruction algorithm to enhance the quality of reconstructed image.The transform is tested in sparse signal and image reconstruction with the undersampled condition.Different sampling ratio is analyzed for quality of recovered images.Firstly four kind of transforms(discrete cosine transform,Hartley transform,fractional Fourier transform and FCBT)are utilized in MPA to reconstruct 1D signal.Hartley transform can combine the real part and imaginary part of Fourier transform.A weighting coefficient is designed to search a best output result for this algorithm.In addition,the MPA in the domains of Fourier transform,Hartley transform and FCBT is checked for sparse image reconstruction.FCBT can generate a better result by choosing suitable phase functions and a fractional order.An iterative image reconstruction in FCBT domain is given.Here several output intensity patterns are obtained by using various fractional orders of FCBT.These patterns serve as the input reference information of the iterative algorithm.The object image is recovered by running constructed parallel calculation processes.The two computational schemes are researched by different reconstruction task.To improve the low convergence phenomenon for the averaging operation in parallel reconstruction,we select an image fusion algorithm with a self-adaption weighting coefficient to accelerate the iterative algorithm.The error of final result is smaller by taking the changed algorithm.The performance of several methods is validated via digital experiments.The image reconstruction under noise environment is also considered.Noise pollution and data loss are evaluated by altering its intensity with the corresponding control parameters for the robustness this image reconstruction algorithm.