Hopfield neural network based algorithms for image restoration and reconstruction. II. Performance analysis

For pt. I see ibid., vol.48, no.7, p.2105-18 (2000). In this paper, we analyze four typical sequential Hopfield (1982) neural network (HNN) based algorithms for image restoration and reconstruction, which are the modified HNN (PK) algorithm, the HNN (ZCVJ) algorithm with energy checking, the eliminating-highest-error (EHE) algorithm, and the simulated annealing (SA) algorithm. A new measure, the correct transition probability (CTP), is proposed for the performance of iterative algorithms and is used in this analysis. The CTP measures the correct transition probability for a neuron transition at a particular time and reveals the insight of the performance at each iteration. The general properties of the CTP are discussed. Derived are the CTP formulas of these four algorithms. The analysis shows that the EHE algorithm has the highest CTP in all conditions of the severity of blurring, the signal-to-noise ratio (SNR) of a blurred noisy image, and the regularization term. This confirms the result in many previous simulations that the EHE algorithms can converge to more accurate images with much fewer iterations, have much higher correct transition rates than other HNN algorithms, and suppress streaks in restored images. The analysis also shows that the CTPs of all these algorithms decrease with the severity of blurring, the severity of noise, and the degree of regularization, which also confirms the results in previous simulations. This in return suggests that the correct transition probability be a rational performance measure.

[1]  Yi Sun.  Hopfield neural network based algorithms for image restoration and reconstruction. I. Algorithms and simulations , 2000, IEEE Trans. Signal Process..

[2]  Guy Demoment,et al.  Image reconstruction and restoration: overview of common estimation structures and problems , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Eric Goles Ch.,et al.  Decreasing energy functions as a tool for studying threshold networks , 1985, Discret. Appl. Math..

[4]  Jehoshua Bruck.  On the convergence properties of the Hopfield model , 1990, Proc. IEEE.

[5]  Aggelos K. Katsaggelos,et al.  Image restoration using a modified Hopfield network , 1992, IEEE Trans. Image Process..

[6]  B. K. Jenkins,et al.  Image restoration using a neural network , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  Yi Sun.  Eliminating-highest-error and fastest-metric-descent criteria and iterative algorithms for bit-synchronous CDMA multiuser detection , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[8]  Yi Sun,et al.  An eliminating highest error criterion in Hopfield neural network for bilevel image restoration , 1992, [Proceedings] Singapore ICCS/ISITA `92.

[9]  Yi Sun,et al.  Improvement on performance of modified Hopfield neural network for image restoration , 1995, IEEE Trans. Image Process..

[10]  H.-J. Liu,et al.  Blind bilevel image restoration using Hopfield neural networks , 1993, IEEE International Conference on Neural Networks.

[11]  Joseph W. Goodman,et al.  A generalized convergence theorem for neural networks , 1988, IEEE Trans. Inf. Theory.

[12]  Yi Sun.  Search algorithms based on eliminating-highest-error and fastest-metric-descent criteria for bit-synchronous CDMA multiuser detection , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[13]  Yi Sun.  A generalized updating rule for modified Hopfield neural network for quadratic optimization , 1998, Neurocomputing.

[14]  José M. N. Leitão,et al.  Sequential and parallel image restoration: neural network implementations , 1994, IEEE Trans. Image Process..

[15]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[16]  Yi Sun,et al.  A modified Hopfield neural network used in bilevel image restoration and reconstruction , 1992, [Proceedings] Singapore ICCS/ISITA `92.