Research On SPECT Reconstruction Algorithm Based On Model-based Deep Learning

Single-photon emission computed tomography（SPECT）is a non-invasive molecular imaging technique that has played an important role in fields such as oncology and cardiovascular disease.This technology reconstructs the distribution of the tracer by detecting the projection of the high-energy photons emitted when the radioactive tracer introduced into the patient decays,and obtains the biochemical information of the tissues and organs by using the difference in radioactivity between different tissues.Changes in this information often precede macroscopic structural changes,and therefore have advantages for early detection and diagnosis of certain diseases.The process of reconstructing the tracer distribution from the projection data of emitted photons at different angles is an ill-posed inverse problem.Given an instance of projection data,the corresponding distribution is not unique but can only be described by probability.Finding the most suitable solution to this model is a long-standing research direction,with the goal of finding a distribution that is closer to the real distribution,while suppressing noise and preserving details.The Preprocessing Alternate Projection Algorithm（PAPA）is a traditional iterative class of algorithms that can be used for SPECT reconstruction.It iteratively reconstructs SPECT by solving a model constructed by minimizing penalized maximum likelihood estimation.PAPA starts from an estimated distribution,and continuously compares and corrects its current projection value with the actual measured value.According to the specific imaging situation,it introduces a priori constraints to control and correct noise,artifacts,smoothness,etc.,gradual iteration,and seeks to converge to the optimal solution under the guidance of the optimization criterion.PAPA models the model physically,manually designs and selects fixed fitting terms and penalty terms,and the solution has generalization and stability.However,the selection of regularization and model parameters is completely dependent on manual design in the early stage and cannot be optimized from the data.It is a complete model-based approach.In recent years,deep learning methods are also commonly used in various fields.Deep learning methods are usually used for nonlinear function approximation under weak assumptions and are fully data-based methods.When used for SPECT reconstruction,the network structure is used end-to-end to learn a mapping from projected data to the true distribution,or to learn a mapping of distribution estimates to the true distribution,without the need to manually design models and parameters,and fully autonomously obtain and Optimize parameters.However,pure data-based deep learning methods lack the constraints brought by model design.If there is no feedback mechanism that can ensure data consistency,it usually requires a large amount of training data and large network structures.Difficult to guarantee its generalization and stability.Therefore,in view of the problems of the above two methods,this thesis proposes a model-based deep learning method for SPECT reconstruction,aiming to combine the generalization and stability of PAPA and the ability of deep learning methods to obtain optimization from data.This thesis includes research in the following areas:The multiple iterative loops of the preprocessing alternating projection algorithm are constructed as a recurrent network,and a multi-convolutional layer is used in the training phase to learn a general penalty term through the data set,which implies the combined action of multiple steps contained in the original PAPA algorithm,and automatically optimize the parameters from the training data without manual design.In the testing phase,it is computed in the same way as the original iterative algorithm,but reconstructed using the new optimization penalty terms learned from the dataset.This makes the iterative results closer to the actual distribution,and at the same time,the number of iterations is significantly reduced,which improves the convergence speed of PAPA,and is difficult to achieve by manual design.At the same time,in this method,the system matrix correlation operation is isolated separately and only used as a variable input,which is excluded from the backpropagation path,reducing the impact of a large system matrix on training time.The processing of the operation related to the system matrix in the above method alleviates the problem of excessive training time to a certain extent,but compared with the pure deep learning method,the training time is still longer.This thesis investigates another network structure that extends the model-based deep learning approach to address further the impact of large system matrices and iterative formats on training time.The preprocessing alternating projection algorithm is iterated in multiple steps to form a deep structure,and multiple convolution layers are used to replace several iterations at the end,in order to gain learning ability.At the same time,the convolution structure is only at the end,so that the gradient calculation backpropagation during training only needs to pass through the end training structure without going through the entire previous iteration process,so that the training time is not affected by the previous iteration length and the calculation related to the system matrix.It significantly reduces training time.This thesis also explores a purely data-based deep learning approach for SPECT reconstruction as a reference.Based on the current reconstruction results of the preprocessing alternating projection algorithm,an encoder-decoder structured convolutional network is used to learn a mapping from the reconstruction results to the actual distribution so that the reconstruction results gradually approach the actual distribution under the guidance of the loss function.This method does not involve a model and relies on the dataset to train the network to optimize the reconstructed image.It is currently the most common deep learning image processing method.This thesis explores the method of model-based deep learning for SPECT reconstruction,the purpose is to improve the speed and accuracy of SPECT reconstruction while retaining generalization and stability,which has good reference significance and practical prospects in the field of medical image reconstruction.In the future,further cooperation with medical institutions and instrument manufacturers is required to verify the clinical performance of this method.