Abstract

A method of reducing image noise is proposed. Each element of a filtered image is obtained by evaluating a least-squares polynomial that has been fitted to a square or circular region surrounding a corresponding element of the noisy image. This is done by convolving the image with an appropriate filter function that is finite in extent and can be computed once and for all, given the polynomial degree. We derive expressions for such filters of both square and circular symmetry. The method is optimum where image noise is additive and gaussian, and the object has a polynomial form. Noise and object spectra need not be known. The proposed method is compared with Wiener filtering. Implementation is discussed.

© 1972 Optical Society of America

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