| The problem we have outlined in this thesis deals largely with the study of the neural network and optimization theory in the Magnetic Resonance Imaging(MRI) reconstruction with the truncated MR data. Based on neural network, two types of stable MR reconstruction algorithms are proposed.In the practical MRI system, especially in the situation that requires high-speed imaging, limited by the physical technology and temporal request, the samples of data is finite. Generally, in the phase coding direction, there are 128 points or more less. The data set is truncated, which makes the conventional Fourier transform method not the most optimal both in the signal-to-noise ratio (SNR) and the image resolution. There are serious truncation artifacts when the conventional Fourier transform method is used to reconstruct directly, which is not enough to be accepted as the correct reconstruction result.To reconstruct magnetic resonance image with incomplete sampled data is an ill-posed problem to reconstruct the initial signal from the partial data of Fourier transform in nature. To solve such problem, the critical procedure is to recruit some acceptable functional constrain in order to restrict the solution subspace. Such method may transfer the ill-posed problem'to be posed, that make it possible to find out the most suitable optimal solution hi all feasible solutions.The basic principle of MRI and fundamental image reconstruction algorithms are reviewed as the first part of this thesis. Then we develop two types reconstruction algorithms based on neural network from different point of view. Utilizing the nonlinear and non-sensitivity to noise characteristics of neural network, these reconstruction algorithms combine the known constraint and regulation condition in order to improve the non-adaptability of reverse problem. So the image reconstruction of small MR data set is transformed into the optimization problem. The known constraints are used to estimate the un-sampled signal. It restrains the Gibbs circle artifacts effectively and the image resolution is unproved. Such result cannot be assimilated with the reconstruction from the conventional Fourier transform method.Chapter 2 introduces the basic principle of MRI, and the Bloch equation and some basic imaging algorithms are included. The discrete FID signal model used in this thesis is discussed as the foundation of the following research.Beginning with the expatiation of image reconstruction problem, Chapter 3 discusses the conventional Fourier transform method and its limitation. The reason of the Gibbs circle artifacts formation and the data-window method are studied. At theend of this part, the project reconstruction algorithm is introduced briefly.In chapter 4, the problem of MR image reconstruction is transformed into the maximum entropy problem under the data coherence constraint. Based on the analysis of the principle of the MR image reconstruction with the maximum entropy neural network, the conjugate complex maximum entropy neural network reconstruction algorithm, which combines the Hopfield neural network and maximum entropy principle, is proposed. It employs the entropy of magnetic resonance image as the cost function. Under the constraint of data coherence, the selected solution may make the entropy of the reconstructed image maximum, and the image obtained is the smoothest image that satisfies the observed data coherence.Based on the extrapolation theory, the multilayer perception is employed as the estimator of the extrapolated data, and a new reconstruct method with such extrapolated data is presented in chapter 5. The adaptive motion of reliable region strategy named LMBP perceptron reconstruction algorithm and regulated complex perceptron reconstruction algorithm may converge in the whole area. They can converge quickly and are of satisfied stability.To be point out, our work will deepen the neural network application in the field of MRI reconstruction with small data set. With the development of EPI and fMRI,the potenti...
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