Annealed Hopfield Neural Network with Moment and Entropy Constraints for Magnetic Resonance Image Classification

摘要

This paper describes the application of an un- supervised parallel approach called the Annealed Hopfield Neural Network (AHNN) using a modified cost function with moment and entropy preservation for magnetic resonance image (MRI) classification. In the AHNN, the neural network architecture is same as the original 2-D Hopfield net. And a new cooling sched- ule is embedded in order to make the modified energy function to converge to an equilibrium state. The idea is to formulate a clus- tering problem where the criterion for the optimum classification is chosen as the minimization of the Euclidean distance between training vectors and cluster-center vectors. In this article, the intensity of a pixel in an original image, the first moment com- bined with its neighbors, and their gray-level entropy are used to construct a 3-component training vector to map a neuron into a two-dimensional annealed Hopfield net. Although the simulated annealing method can yield the global minimum, it is very time- consuming with asymptotic iterations. In addition, to resolve the optimal problem using Hopfield or simulated annealing neu- ral networks, the weighting factors to combine the penalty terms must be determined. The quality of final result is very sensitive to these weighting factors, and feasible values for them are dif- ficult to find. Using the AHNN for magnetic resonance image classification, the need of finding weighting factors in the energy function can be eliminated and the rate of convergence is much faster than that of simulated annealing. The experimental results show that better and more valid solutions can be obtained us- ing the AHNN than the previous approach in classification of the computer generated images. Promising solutions of MRI segmen- tation can be obtained using the proposed method. In addition, the convergence rates with different cooling schedules in the test phantom will be discussed.