Image restoration using truncated SVD filter bank based on an energy criterion

Image restoration is formulated using a truncated singular-value-decomposition (SVD) filter bank. A pair of known data patterns is used for identifying a small convolution operator. This is achieved by matrix pseudo-inversion based on SVD. Unlike conventional approaches, however, here SVD is performed upon a data-pattern matrix that is much smaller than the image size, leading to an enormous saving in computation. Regularisation is realised by first decomposing the operator into a bank of sub-filters, and then discarding some high-order ones to avoid noise amplification. By estimating the noise spectrum, sub-filters that produce noise energy more than that of useful information are abandoned. Therefore high-order components in the spectrum responsible for noise amplification are rejected. With the obtained small kernel, image restoration is implemented by convolution in the space domain. Numerical results are given to show the effectiveness of the proposed technique.