Digital image restoration by Wiener filter in 2D case

Modern digital technology has made it possible to manipulate multi-dimensional signals with systems that range from simple digital circuits to advanced parallel computers. The goal of this manipulation can be divided into three categories:
• Image Processing image in → image out.
• Image Analysis image in → measurements out.
• Image Understanding image in → high-level description out.Further, we will restrict ourselves to two-dimensional (2D) image processing although most of the concepts and techniques that are to be described can be extended easily to three or more dimensions. The Wiener filter is a solution to the restoration problem based upon the hypothesized use of a linear filter and the minimum mean-square (or rms) error criterion. In the example given below the image a[m, n] was distorted by a bandpass filter and then white noise was added to achieve an SNR = 30 dB.