The Curve-driven-based Discretization Of Forward Model And The DCWT-TV Based Regularization Reconstruction Algorithm In Photoacustic Tomography

Photoacoustic tomography is a biomedical imaging modality with both optical imaging contrast and acoustic imaging resolution,which is based on the photoacoustic effect.It overcomes the limitation of penetration depth and spatial resolution of optical imaging with ultrasonic signals,and overcomes the shortcomings of low contrast of ultrasonic imaging by using tissue light absorption characteristics.Therefore,photoacoustic tomography(PAT)has become the frontier of biomedical imaging research in recent years.In which,the image to be reconstructed is the initial sound pressure distribution of the photoacoustic effect,and then,researchers can obtain the optical characteristic distribution of the biological tissue based on this reconstruction result.The model-based PAT reconstruction is widely used because it is not limited by the spatial distribution of ultrasonic transducers and has good anti-noise performance.In the model-based photoacoustic reconstruction,the image reconstruction process can be divided into two steps: first,the forward propagation model of the ultrasound is discretized,and then the initial sound pressure distribution in tissues is retrieved based on the discrete model.As a result,the model-based photoacoustic imaging results are affected by the discretization accuracy of the forward process and the performance of the inverse inversion algorithm.The interpolation-based forward model discretization method is widely used because of its simple and fast implementation.The disadvantage of this method is that the accuracy of model discretization is influenced by the number of interpolated points and the quadratic approximation error which is introduced in the interpolating process.The inversion problem of the discrete model is an ill-posed problem.In order to obtain a good approximate solution,the researchers proposed a variety of regularization image reconstruction algorithm.However,these regularization reconstruction algorithms either result in loss of the important structure of the image or poor smoothing performance of the image.Thus,the research contents of this dissertation are as follows.Because the discretization accuracy of the discretization method based on interpolation is affected by interpolation points and the quadratic error that introduced by the interpolation process,we propose to use an curve-driven-based discretization method to avoid the interpolation process and improve the precision of discretization.To meet the problem that the existing regularization reconstruction methods can not preserve the important structure information as well as smoothing image,we propose to combining the sparse regularization that based on the Haar wavelets transform and the dis-crete cosine transform,and the total variation regularization to forming a new regularization method for image reconstruction.The ultimate goal of this Ph.D.research is to construct an image reconstruction algorithm that preserves the important structure information as well as the smoothness of the image.The main results of this research are as follows:1.The core of the discretization of the ultrasonic forward propagation model is the discretization of the integral part of the ultrasonic transmission equation.In the interpolationbased discretization model,the coverage angle of the integral curve is first discretized uniformly,and then the discrete points of the integral curve are located.The contribution of the pixel to the discrete integral is determined by interpolating the discrete points and the discrete coverage angle.This results in an integral curve with the same coverage angle and different radii has different sampling densities.In addition,the interpolation process also results in an quadratic approximation errors.These two factors make the precision of interpolation-based discretization worse.To solve this problem,we reconsider the integration process.Since the discrete integral can be expressed as the weighted sum of the pixels through which the integral curve passes,and the weight corresponding to each pixel is the circumferential coverage angle corresponding to the part of the integral curve intersecting the pixel.We propose a fast method to compute these weight,and we call this forward model discretization method the curve-driven-based model discretization method.Compared with the interpolation-based discretization method,the curve-driven-based method does not require interpolation and involve the discretization of the integral curve,so its accuracy is higher.The results of numerical simulation,simulation and mouse in vivo show that the proposed forward discretization method has higher forward precision and anti-noise performance.Although the time consumption to calculating the model matrix with the proposed method is more than that of interpolation-based method,we think it is acceptable.2.Model-based photoacoustic tomographic reconstruction is a morbid problem,and researchers have proposed different regularization reconstruction algorithms to alleviate this problem.Among which,Tikhonov regularization method,regularization method based on sparsity,regularization method based on TV and iterative regularization method based on LSQR are the most widely used.Tikhonov regularization reconstruction algorithm can obtain a good noise suppression performance and loss of high-frequency components.The reconstruction algorithm based on sparse regularization can save the discontinuous structure of image,such as edge,and its disadvantages are noise suppression.The image reconstruction algorithm based on TV regularization can save the image edge well and suppress the local noise,but this method may cause the image detail to be lost.Based on the above considerations,we propose to combine a sparse regularization term and a TV regularization term to form a new regularization reconstruction algorithm.In this study,we combine Haar wavelet transform,discrete cosine transform and TV regularization term to form a DCWTTV regularization reconstruction algorithm.Among them,the subject of the discrete cosine transform is the low frequency component of Haar wavelet transform,and the sparseness of the solution is forced by using the L1 norm of which transformed coefficients.This is used to preserve the discontinuous structure information of the solution.TV regularization term is used to preserve the edge of the image,and to smooth the image locally.We verified the performance of the DCWT-TV regularization reconstruction algorithm by using simulation experiments,phantom experiments and mouse experiments,and compared it with the LSQR,TV regularization,Haar wavelet sparse regularization and Tikhonov regularization methods.The results show that the proposed DCWT-TV regularization algorithm has better noise suppression and image discontinuity preservation performance.