Tsutomu Matsuura

Approximate and analytical inversion formulas in heat conduction on multidimensional spaces

In this paper we shall give practical real inversion formulas of heat conduction on multidimensional spaces and show their numerical experiments by using computers.

Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces

We shall discuss the relations among sampling theory (Sinc method), reproducing kernels and the Tikhonov regularization. Here, we see the important difference of the Sobolev Hilbert spaces and the Paley–Wiener spaces when we use their reproducing kernel Hibert spaces as approximate spaces in the Tikhonov regularization. Further, by using the Paley–Wiener spaces, we shall illustrate numerical experiments for new inversion formulas for the Gaussian convolution as a much more powerful and improved method by using computers. In this article, we shall be able to give practical numerical and analytical inversion formulas for the Gaussian convolution that is realized by computers.

Dirichlet principle using computers

In this article we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show the numerical experiments by using computers. Our method is based on the Dirichlet principle by combinations with generalized inverses, Tikhonovs regularization and the theory of reproducing kernels.

Numerical solutions of the poisson equation

In this article we shall give practical and numerical solutions of the Poisson equation on multidimensional spaces and show their numerical experiments by using computers.

Measurement of Space Variant PSF for Restoring Degraded Images by Security Cameras

Images recorded by a security camera have often severely degraded due to dirty lens or secular distortion of the recording system. To restore these images, the fully determination of space variant point spread function (PSF) is required. To measure PSF, we used a liquid crystal display. We made some experiment to restore the images by a CCD camera with intentionally distorted optics

Importance of Developing Image Restoration Techniques for Security Cameras under Severe Conditions

A concept, which was proposed and has been pursued by the authors for restoring the images of a suspected person taken by a security camera, is reviewed. In the concept, the peculiar facts concerning the security camera system that all the things in the image except the suspected person itself are usually preserved and that can be used for investigations are to be used as fully as possible. The authors have launched a project in which techniques based on the concept are developed for the police. In the project, some methods of restoring an image of a persons figure taken by a camera with dirty lens have been developed. The importance of pursuing the proposed concept is discussed from the viewpoints of not only the novelty in image processing technology but also the viewpoints of the efficiency in criminal investigation and social security

Image Restoration for Security Cameras with Dirty Lens under Oblique Illumination

An approach for restoring the images of a suspected person taken by a security camera with dirty lens is proposed. In the approach, the peculiar facts concerning the security camera system that all the things in the image except the suspected person itself are usually preserved and that can be used for investigations are to be used as fully as possible. As the first trial for realizing the proposed approach, a method of restoring an image of a persons face taken by a camera with dirty lens under strong oblique illumination is proposed and its practical application is demonstrated experimentally. The importance of pursuing the proposed approach is discussed from the viewpoints of not only the novelty in image processing technology but also the viewpoints of the efficiency in criminal investigation and social security.

General Integral Transforms by the Concept of Generalized Reproducing Kernels

In Saitoh (Proc Am Math Soc 89:74–78, 1983), the general integral transforms in the framework of Hilbert spaces were combined with the general theory of reproducing kernels by Aronszajn (Trans Am Math Soc 68:337–404, 1950) and many applications were developped, for example, in Saitoh (Integral transforms, reproducing kernels and their applications, vol 369, Addison Wesley Longman, Harlow, 1997). The basic assumption here that the integral kernels belong to some Hilbert spaces. However, as a very typical integral transform, in the case of Fourier integral transform, the integral kernel does not belong to L2(R) and, however, we can establish the isometric identity and inversion formula.On the above situations, we will develop some general integral transform theory containing the Fourier integral transform case that the integral kernel does not belong to any Hilbert space, based on the recent general concept of generalized reproducing kernels in Saitoh and Sawano (Generalized delta functions as generalized reproducing kernels, manuscript; General initial value problems using eigenfunctions and reproducing kernels, manuscript).

Dirichlet’s Problem by Using Computers with the Theory of Reproducing Kernels

In this paper we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show their numerical experiments by using computers. Our method is based on the Dirichlet principle by combinations with generalized inverses, Tikhonov’s regularization and the theory of reproducing kernels.

Separation and Reproduction of Mixed Images Using 2-D Complex Wavelet Transform

The differences method between 1-D wavelet transform and 2-D wavelet transform in image processing is discussed. Both proposed method uses the quotient of complex valued time-frequency information of observed signals to detect the number of sources. No less number of observed signals than the detected number of sources is needed to separate sources. The assumption on sources is quite general independence in the time-frequency plane, which is different from that of independent component analysis. Using the same given Algorithm and parameters for both method, the result on separated images are compared.