Projection Filter Regularization Of Ill-Conditioned Problem

Hidemitsu Ogawa

doi:10.1117/12.941482

10 September 1987 Projection Filter Regularization Of Ill-Conditioned Problem

Hidemitsu Ogawa

Proceedings Volume 0808, Inverse Problems in Optics; (1987) https://doi.org/10.1117/12.941482
Event: Fourth International Symposium on Optical and Optoelectronic Applied Sciences and Engineering, 1987, The Hague, Netherlands

Abstract

The usual regularization theory for posed ill-problem may be called the regularization of Weierstrass type in the context of approximation theory. On the contrary, this paper proposes the regularization of Chebyshev type, named the "projection filter regulariza-tion". In the absence of noise, the projection filter provides the best approximation Pf to the real solution f, where P is the orthogonal projection operator onto a subspace. In the presence of noise, it provides the best approximation to the individual Pf in the average sense with respect to noise. A general form of projection filter is obtained. Properties of projection filter are discussed in detail.

Citation Download Citation

Hidemitsu Ogawa "Projection Filter Regularization Of Ill-Conditioned Problem", Proc. SPIE 0808, Inverse Problems in Optics, (10 September 1987); https://doi.org/10.1117/12.941482

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