Stagewise Processing in Error-correcting Codes and Image Restoration

Hidetoshi Nishimori Department of Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8551, Japan nishi@stat.phys.titech.ac.jp Abstract We introduce stagewise processing in error-correcting codes and image restoration, by extracting information from the former stage and using it selectively to improve the performance of the latter one. Both mean-field analysis using the cavity method and simulations showthat it has the advantage of being robust against uncertainties in hyperparameter estimation. 1 Introduction In error-correcting codes [1] and image restoration [2], the choice of the so-called hyperparameters is an important factor in determining their performances. In error correction, they determine the statistical significance given to the paritychecking termsand the received bits. Similarly in image restoration, they determine the statistical weights given to the prior knowledge and the received data. It was shown, by the use of inequalities, that the choice of the hyperparameters is optimal whenthere is a match between the source and model priors [3].