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Wiener filtering illustrations 6.011, Spring 2018 Lec 21 1 Unconstrained Wiener filter structure - m x m y y [ n ] x [ n ] + + h [] 2 Unconstrained Wiener filter solution - m x m y D yx ( e j ) H ( e j ) = x [ n ] y [ n ] + + D xx (

Wiener filtering illustrations 6.011, Spring 2018 Lec 21 1
Unconstrained Wiener filter structure - m x m y y [ n ] x [ n ] + + h [·] 2
Unconstrained Wiener filter solution - m x m y D yx ( e j Æ ) H ( e j Æ ) = x [ n ] y [ n ] + + D xx ( e j Æ ) 3
E.g.: Wiener “deconvolution” of a noisy blurred signal v [ n ] y [ n ] y [ n ] G [ z ] + H [ z ] r [ n ] x [ n ] Known, stable system Wiener f lter 4
E.g.: Wiener deconvolution of a noisy blurred image** Two-dimensional convolution + noise: x [ k, l ] = P P j g [ i, j ] y [ k − i, l − j ] + v [ k, l ] i **From 2007 Mathworks blog post by 5 Prof. Stan Reeves, ECE Dept., Auburn University
Wiener deconvolution of a noisy blurred image Mathworks blog posts by: Prof. Stan Reeves, ECE Dept., Auburn University Reeves, Stan. "Digital image processing using MATLAB: reading image files". MathWorks. Sept. 27, 2011. Reeves, Stan. "Image deblurring – Wiener filter." MathWorks. Nov. 2, 2007. 6
MIT OpenCourseWare https://ocw.mit.edu 6.011 Signals, Systems and Inference Spring 201 8 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. 7

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