In this manuscript, we discuss Markov random fields and belief propagations, sum-product algorithm and max-product algorithm, that construct a framework of the probabilistic image processing. The concepts of these two topics have occupied an important place in the field of the computer vision. We see fundamental mathematics of probabilistic image processing from the viewpoint of Markov random fields and belief propagations, and see how to implement probabilistic image processing systems through an example of de-noising filter.

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Recent advances in measurement techniques allow us to obtain a large quantity of imaging data in various natural science fields. These data can be analyzed by Markov random field (MRF) models which have made progress in information science. We can estimate hyperparameters in our MRF model, which is a probabilistic one, by the framework of Bayesian inference. When our MRF model is applied to diffusion systems which often appear in the natural sciences, a hyperparameter is an important parameter which corresponds to the diffusion coefficient. Thus, in this study, we calculate not only a point estimate but also a distribution estimate of hyperparameters to evaluate estimation reliability.

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An inference technique in which a posterior probability calculated by the Bayesian theorem is used is called Bayesian inference. We introduce an image super-resolution technique based on Bayesian inference. The compound Bayesian super-resolution proposed by Kanemura et al. is explained in particular. In Bayesian super-resolution, subpixel details can be reproduced because shifts and rotations of observed images are utilized positively. Furthermore, edge reproduction is realized by the line process in compound Bayesian super-resolution. In this paper, we describe the outline of compound Bayesian super-resolution and show experimental results.

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Recently, many sparsity based information processing methods have been proposed. We call them "sparse modeling" here. The most popular methods of sparse modeling are LASSO and compressed sensing. Here, we formulate LASSO from a Bayesian viewpoint, and explain how we apply the idea of sparse modeling to X-ray diffraction imaging.

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Studies on improving performance of magnetic resonance imaging (MRI) via focusing on and making use of sparsity of images under appropriate sparsifying basis. A mathematical foundation of such studies is compressed sensing, which allows us to solve underdetermined linear equations assuming sparsity of the solution. MRI image reconstruction on the basis of sparsity can be regarded as an example of the innovation in the field of medical image engineering, in which one separates data acquisition and image reconstruction. Magnetic resonance fingerprinting can be regarded as an approach which advances this idea further in the context of MRI, and a combination of magnetic resonance fingerprinting and compressed sensing is studied as well in order to further improve performance.

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To improve cardiovascular MDCT imaging workflow, we developed an interpretation support system for cardiovascular MDCT imaging. The system can record information regarding the disease's location, nature of the plaque, and presence or absence of calcification. And also we developed an image classification method utilizing DICOM Tag to help radiologists to choose images for reading. To investigate whether a newly developed support system could reduce the time taken by radiologists to read coronary artery MDCT images, as well as improve diagnostic accuracy, a total of 20 studies (10 initial and 10 follow-up MDCT) were reviewed. As a result, the reading time for both readers was reduced by about 20%. The diagnostic concordance rate for disease's location was increased from 92% to 100%

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Pulmonary nodules with ground glass opacity (GGO) in lung CT images are difficult to differential diagnosis, and follow-up are often performed. In cases of follow-up, the present CT images are compared with past CT images, and it is necessary to evaluate the changes quantitatively. So, we have developed a volumetric segmentation algorithm of pulmonary nodules with GGO on CT images. Nodules with GGO, especially pure-GGO, are difficult to define a threshold value. Therefore, our algorithm does not define a threshold value. In our algorithm, the first step is to emphasize CT images using the sigmoid function. Next, the nodule is roughly segmented with background subtraction. Finally the nodule without vessels is decided by morphological operation, etc. For evaluation of our algorithm, we selected nodules with GGO from the dataset provided by LIDC (The Lung Image Database Consortium). In this paper, we illustrate some experimental result w hich applied our algorithm.

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In laparoscopic surgery, to identify the location of the lesion and the blood vessels inside organs, an ultrasound probe which can be inserted through small incision is used. However, since surgeons must observe the laparoscopic and t ultrasound images at the same time, it is difficul to understand the correspondence between the ultrasound image and the real space. Therefore, to recognize the correspondence between the two images intuitively, we developed a system for overlaying an ultrasound image on the laparoscopic image. Since the tip of the probe is flexed freely, we got the probe tip position and orientation using a method for detecting the probe angle of laparoscopic image. As results of experiment using a wire phantom, overlaying error of ultrasound images was 6.9 pixel. Further, the rate of probe angle detection was 83.1% in animal experiments performed laparoscopically.

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A numerical simulator for MRI experiments is useful in improving the efficiency of the pulse sequence and hardware development. However, a diffusion-weighted imaging (DWI) simulator for a human-brain-sized model has not yet been developed because such a simulator would require a large amount of computing costs. We recently developed a DWI simulator by applying new acceleration techniques, and managed to reduce the computation time to a few hours. However, this computation time increases with an increasing requirement for the enhancement of the simulator's functionality. To meet this requirement, we herein propose the use of compressed sensing (CS) as an additional acceleration technique. First, we fixed an appropriate data sampling ratio from the viewpoint of image quality, and applied it to the generation of an MR signal so as to reduce the simulation time to 30%. We then applied CS to simulate DWI with a fluctuating motion probing gradient (MPG). As a result, we found that the DWI simulator using CS with a 30% data sampling ratio was effective in estimating the relationship between the amount of MPG fluctuation and the image degradation.

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This paper describes the current status and challenges of Ai. At present, Ai is performed to prevent missing the crime or when medical-related death is suspected, but it is going to be a system which spreads out over the wider society in the future. Since die of the human occurs only once, Ai is also performed only once. It is possible in Japan, anyone can receive the Ai anywhere. There exist no other way other than Ai to investigate the cause of death fairly.

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