Deconvolution using natural image priors- Lecture notes

If the matrix C f is a full rank matrix, and no noise is involved in the imaging process, the simplest approach to deconvolve y is to invert C f and define x = C −1 f y. Or in the frequency domain, X(ν,ω) = Y (ν,ω)/F(ν,ω) This, however, is very rarely stable enough. For example, the inverse is not defined in frequencies (ν,ω) for which F(ν,ω) = 0. Even in case |F(ν,ω)| is not exactly 0 but small, the inverse is very sensitive to noise. That is, if the Y we are observing includes some noise Y (ν,ω) = F(ν,ω)X(ν,ω) + n, than the inverse will produce Y (ν,ω)/F(ν,ω) = X(ν,ω)+n/F(ν,ω), so, when |F(ν,ω)| is small the noise contribution is increased.