Atsunori Kanemura

Superresolution with compound Markov random fields via the variational EM algorithm

This study deals with a reconstruction-type superresolution problem and the accompanying image registration problem simultaneously. We propose a Bayesian approach in which the prior is modeled as a compound Gaussian Markov random field (MRF) and marginalization is performed over unknown variables to avoid overfitting. Our algorithm not only avoids overfitting, but also preserves discontinuity in the estimated image, unlike existing single-layer Gaussian MRF models for Bayesian superresolution. Maximum-marginal-likelihood estimation of the registration parameters is carried out using a variational EM algorithm where hidden variables are marginalized out, and the posterior distribution is variationally approximated by a factorized trial distribution. High-resolution image estimates are obtained through the process of posterior computation in the EM algorithm. Experiments show that our Bayesian approach with the two-layer compound model exhibits better performance both in quantitative measures and visual quality than the single-layer model.

Sparse Bayesian Learning of Filters for Efficient Image Expansion

We propose a framework for expanding a given image using an interpolator that is trained in advance with training data, based on sparse Bayesian estimation for determining the optimal and compact support for efficient image expansion. Experiments on test data show that learned interpolators are compact yet superior to classical ones.

Edge-preserving Bayesian image superresolution based on compound Markov random fields

This study deals with image superresolution problems simultaneously with accompanying image registration problems. The goal of superresolution is to generate a high resolution image by integrating low-resolution degraded observed images. We propose a Bayesian approach whose prior is modeled as a compound Gaussian Markov random field (MRF). This approach is advantageous in preserving discontinuity in the original image, in comparison to the existing single-layer Gaussian MRF models. Maximum-marginalized-likelihood estimation of the registration parameters is carried out by a variational EM algorithm where hidden variables are marginalized out and the posterior distribution is approximated by a factorized trial distribution. High resolution image estimates are obtained as by-products of the EM algorithm. Experiments show that our Bayesian approach with two-layer compound models exhibits better performance in terms of mean square error and visual quality than the single-layer model.

Maximum a posteriori X-ray computed tomography using graph cuts

We develop maximum a posteriori (MAP) method for X-ray computed tomography (CT). We present a mixture prior to represent the knowledge that the human body is composed of a finite number of material kinds whose CT values are roughly known in advance. The tomographic image and material classes are simultaneously estimated in an alternating manner, where a graph cut algorithm is used to minimize the MAP objective function. Experiments show that the proposed algorithm performs better than the existing methods in severe situations where samples are limited or metals are inserted into the body.

Hyperparameter Estimation in Bayesian Image Superresolution with a Compound Markov Random Field Prior

We address the hyperparameter estimation problem in Bayesian image superresolution with a compound Gaussian Markov random field (MRF) prior. Superresolution aims at reconstructing a high-resolution (HR) image from low-resolution degraded observations, and the compound MRF enables edge-preserving superresolution owing to the additional layer of edge representation. In addition to the regularization hyperparameters, the compound model has an additional hyperparameter of the edge bias that controls the probability of edge presence. We estimate all the hyperparameters, the registration parameters, and the HR image by means of minimizing variational free energy under the assumption of a factorized posterior. Experiments show that automatic determination of the hyperparameters including the bias and the regularization parameters, as well as edge- preserving superresolution of the HR image, is successfully accomplished by the proposed method.

Bayesian image superresolution and hidden variable modeling

Superresolution is an image processing technique that estimates an original high-resolution image from its low-resolution and degraded observations. In superresolution tasks, there have been problems regarding the computational cost for the estimation of high-dimensional variables. These problems are now being overcome by the recent development of fast computers and the development of powerful computational techniques such as variational Bayesian approximation. This paper reviews a Bayesian treatment of the superresolution problem and presents its extensions based on hierarchical modeling by employing hidden variables.

Image Superresolution under Spatially Structured Noise

We develop an image superresolution method that can deal with spatially structured noise added to an original image. Such a structured noise process can be understood as a model for possible occlusions such as clouds in the sky or stains on the lens, and is modeled as spin glasses. The original high-resolution image underlying multiple low-resolution observed images and the hidden noise structure are estimated via a variational learning algorithm. Experiments show that our superresolution method can outperform other methods that do not assume structured noise.

Bayesian X-ray computed tomography using material class knowledge

We propose a new reconstruction procedure for X-ray computed tomography (CT) based on Bayesian modeling. We utilize the knowledge that the human body is composed of only a limited number of materials whose CT values are roughly known in advance. Although the exact Bayesian inference of our model is intractable, we propose an efficient algorithm based on the variational Bayes technique. Experiments show that the proposed method performs better than the existing methods in severe situations where samples are limited or metal is inserted into the body.

Superresolution from Occluded Scenes

We propose a Bayesian image superresolution method that estimates a high-resolution background image from a sequence of occluded observations. We assume that the occlusions have spatial and temporal continuities. Such assumptions would be plausible, for example, when satellite images are occluded by clouds or when a tourist site is obstructed by people. Although the exact inference of our model is difficult, an efficient superresolution algorithm is derived by using a variational Bayes technique. Experiments show that our superresolution method performs better than existing methods that do not assume the occlusions or that assume the occlusions but do not assume the temporal continuities of the occlusions.

Learning color image expansion filters

Image expansion by linear filtering is attractive and widely used because of its simplicity and efficiency, and many interpolation methods fall in this category. In this study, we model filtering as linear regression from low- to high-resolution color image patches, and propose a learning-based design method of image expansion filters based on sparse Bayesian estimation. Sparseness is imposed on the filter coefficients to obtain compact supports. Image expansion is formulated as the problem of finding the predictive mean of a high-resolution patch given a low-resolution patch to expand. Since an exact evaluation of the predictive distribution is difficult, variational methods are employed to derive an efficient algorithm. Experiments on test data show that good generalization performance is obtained based on sparse filters and that color modeling improves the expansion quality.