著者

Shoichi Koyama

出版者

ACOUSTICAL SOCIETY OF JAPAN

雑誌

Acoustical Science and Technology (ISSN:13463969)

巻号頁・発行日

vol.41, no.1, pp.269-275, 2020-01-01 (Released:2020-01-06)

参考文献数

33

被引用文献数

5

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Estimating and interpolating a sound field from measurements using multiple microphones are fundamental tasks in sound field analysis for sound field reconstruction. The sound field reconstruction inside a source-free region is achieved by decomposing the sound field into plane-wave or harmonic functions. When the target region includes sources, it is necessary to impose some assumptions on the sources. Recently, it has been increasingly popular to apply sparse representation algorithms to various sound field analysis methods. In this paper, we present an overview of sparsity-based sound field reconstruction methods and also demonstrate their application to sound field recording and reproduction.

著者

Natsuki UENO Shoichi KOYAMA Hiroshi SARUWATARI

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)

巻号頁・発行日

pp.2021EAP1004, (Released:2021-02-25)

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We propose a useful formulation for ill-posed inverse problems in Hilbert spaces with nonlinear clipping effects. Ill-posed inverse problems are often formulated as optimization problems, and nonlinear clipping effects may cause nonconvexity or nondifferentiability of the objective functions in the case of commonly used regularized least squares. To overcome these difficulties, we present a tractable formulation in which the objective function is convex and differentiable with respect to optimization variables, on the basis of the Bregman divergence associated with the primitive function of the clipping function. By using this formulation in combination with the representer theorem, we need only to deal with a finite-dimensional, convex, and differentiable optimization problem, which can be solved by well-established algorithms. We also show two practical examples of inverse problems where our theory can be applied, estimation of band-limited signals and time-harmonic acoustic fields, and evaluate the validity of our theory by numerical simulations.

著者

Natsuki UENO Shoichi KOYAMA Hiroshi SARUWATARI

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)

巻号頁・発行日

vol.E104-A, no.9, pp.1293-1303, 2021-09-01

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We propose a useful formulation for ill-posed inverse problems in Hilbert spaces with nonlinear clipping effects. Ill-posed inverse problems are often formulated as optimization problems, and nonlinear clipping effects may cause nonconvexity or nondifferentiability of the objective functions in the case of commonly used regularized least squares. To overcome these difficulties, we present a tractable formulation in which the objective function is convex and differentiable with respect to optimization variables, on the basis of the Bregman divergence associated with the primitive function of the clipping function. By using this formulation in combination with the representer theorem, we need only to deal with a finite-dimensional, convex, and differentiable optimization problem, which can be solved by well-established algorithms. We also show two practical examples of inverse problems where our theory can be applied, estimation of band-limited signals and time-harmonic acoustic fields, and evaluate the validity of our theory by numerical simulations.