arXiv subjects

Kao Hayashi

Publications and source records attributed to Kao Hayashi.

3 recordsLinked to original sources

arXiv2026

Statistical mechanical evaluation of a spread-spectrum watermarking model with image restoration II AT stability of a hybrid system with message decoding and image

In the previous paper (arxiv.org/abs/1209.4772), we proposed a spread-spectrum watermarking model with image restoration based on Bayes estimation assuming several prior probabilities and adopting the Gaussian channel model to represent attacks from unauthorized users. When an image is generated from the infinite range Ising model, we analyzed the model using the statistical mechanical method, the replica method, and derived the replica symmetric (RS) solution and performed Markov chain Monte Carlo simulations. The theoretical results of the RS solution and the simulation results were in good agreement except for some range of parameters. We treated the informed case where only the original image is known and the blind case where both the original message and the original image are unknown and found that the difference between these cases was small as long as the embedding and attack rates were small. In this paper, we treat the blind case and investigate the de Almeida-Thouless (AT) stability of the RS solution and reveal that the AT stability is broken in the range of parameters where theoretical and simulation results do not agree.

cond-mat.stat-mech↗

arXiv2021

Reconstructing Sparse Signals via Greedy Monte-Carlo Search

We propose a Monte-Carlo-based method for reconstructing sparse signals in the formulation of sparse linear regression in a high-dimensional setting. The basic idea of this algorithm is to explicitly select variables or covariates to represent a given data vector or responses and accept randomly generated updates of that selection if and only if the energy or cost function decreases. This algorithm is called the greedy Monte-Carlo (GMC) search algorithm. Its performance is examined via numerical experiments, which suggests that in the noiseless case, GMC can achieve perfect reconstruction in undersampling situations of a reasonable level: it can outperform the $\ell_1$ relaxation but does not reach the algorithmic limit of MC-based methods theoretically clarified by an earlier analysis. The necessary computational time is also examined and compared with that of an algorithm using simulated annealing. Additionally, experiments on the noisy case are conducted on synthetic datasets and on a real-world dataset, supporting the practicality of GMC.

stat.ML↗

arXiv2019

Statistical mechanical evaluation of spread spectrum watermarking model with image restoration

In cases in which an original image is blind, a decoding method where both the image and the messages can be estimated simultaneously is desirable. We propose a spread spectrum watermarking model with image restoration based on Bayes estimation. We therefore need to assume some prior probabilities. The probability for estimating the messages is given by the uniform distribution, and the ones for the image are given by the infinite range model and 2D Ising model. Any attacks from unauthorized users can be represented by channel models. We can obtain the estimated messages and image by maximizing the posterior probability. We analyzed the performance of the proposed method by the replica method in the case of the infinite range model. We first calculated the theoretical values of the bit error rate from obtained saddle point equations and then verified them by computer simulations. For this purpose, we assumed that the image is binary and is generated from a given prior probability. We also assume that attacks can be represented by the Gaussian channel. The computer simulation retults agreed with the theoretical values. In the case of prior probability given by the 2D Ising model, in which each pixel is statically connected with four-neighbors, we evaluated the decoding performance by computer simulations, since the replica theory could not be applied. Results using the 2D Ising model showed that the proposed method with image restoration is as effective as the infinite range model for decoding messages. We compared the performances in a case in which the image was blind and one in which it was informed. The difference between these cases was small as long as the embedding and attack rates were small. This demonstrates that the proposed method with simultaneous estimation is effective as a watermarking decoder.

cond-mat.stat-mech↗