The basic mathematical problem in computed tomography (CT) is defined as finding a nonnegative solution to a rectangular linear system with a sparse coefficient vector and matrix. The coefficient vector and matrix respectively correspond to acquired projection data and a projection operator based on a discrete Radon transform. As an approach to find a nonnegative solution corresponding to a tomographic image, a continuous method using simultaneous ordinary differential equations has been proposed. The continuous method can produce high-quality images even from an insufficient number of projection data. However, it requires a huge computational cost to obtain a high-quality image because of numerical integration. In this paper, to reduce the image-reconstruction time, we proposed two iterative methods without numerical integration that enable us to reconstruct high-quality CT images without negative pixels. The methods were produced on the basis of a hierarchical alternating least-squares algorithm that is known as a fast solver for nonnegative matrix factorization and conjugate gradient methods that are effective for a linear system. Through numerical experiments, we also discussed the performances of the proposed methods in terms of both the quality of obtained images and the time required to obtain high-quality images.

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This paper is concerned with a pseudo-formal linearization method using Chebyshev expansion and its application to a nonlinear observer for nonlinear scalar-measurement systems. The given nonlinear autonomous dynamic system is linearized into an augmented linear system with respect to a linearization function that consists of polynomials of state variables by a pseudo-formal linearization method using Chebyshev expansion. As an application of this method, a nonlinear observer is discussed. An augmented measurement vector that consists of polynomials of measurement data is introduced and is transformed into an augmented linear one by the pseudo-formal linearization technique using Chebyshev expansion. Thereby, a linear system theory is applied to both the linearized dynamic and measurement systems in order to design a new nonlinear observer. Numerical experiments indicate that the performance of the presented method is superior to that of the previous method.

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It is well known that the Lifting Scheme (LS) allows us to design the fast calculation method of the Discrete Wavelet Transform (DWT). However, unfortunately, the LS can be only adopted for the wavelets having a compact support. For example, Meyer wavelet, which is a famous orthonormal wavelet basis, has no compact support. Additionally, the Complex Discrete Wavelet Transform (CDWT) is steady and useful for many signal processing applications, however, its imaginary part is constructed from the wavelets having no compact support. Therefore, we cannot adopt the LS for these analyses. In this study, we propose the design method of the LS filters for all the orthonormal wavelet bases without relation to having a compact support or not. We adopt our proposed method for the CDWTs using Meyer wavelet and Daubechies 6 wavelet, and confirm their steady analyses and fast calculation speeds.

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In Session 15, the reason why many quanta have spin 1/2 was demonstrated by applying circuit theory to the Dirac equation. In this session, we attempt to apply circuit theory to the Dirac equation from a different viewpoint and determine a model in which electrons and neutrinos are not bound to other quanta and exist independently. We also determine a model of neutrons and protons that have spin 1/2 and can be bound to other quanta and show that this model represents the elements of an asymmetric LC ladder circuit, which can be treated as particles.

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