|ECR 2006 / B-652|
|The sensitive and accurate de-convolution technique to correct for the "penumbral-spread" effect in CT, MR and DF|
Due to the size(s) of the energy source, the detector(s) size, and other second-order factors, a specific-shaped Line Spread Function (LSF), or blurred Edge Response Function (ERF) in the image domain is obtained from a Delta Function or Step Function (SF) in the object domain. This specific-shaped LSF or `blurred’ ERF varies from edge position to edge position.
Mathematically, the ERF can be derived by the convolution of the LSF with the SF. Experimentally, we can derive the “local” LSF from the ERF by a patented De-Convolution Process using a Running Filter Technique, to pinpoint, from the mid-point of the full width half maximum, the true edge position to the sub-pixel accuracy. The original high-resolution feature of the edge-profile may be restored, via an algorithm, by sub-pixel transfer to correct empirically, for this “Penumbral-Spread”. This is performed under strict spatial bandwidth controls to avoid ambiguity (Figure 1).