A novel error metric for parametric fitting of point spread functions

Established work in the literature has demonstrated that with accurate knowledge of the corresponding blur kernel (or point spread function, PSF), an unblurred prior image can be reliably estimated from one or more blurred observations. It has also been demonstrated, however, that an incorrect PSF specification leads to inaccurate image restoration. In this paper, we present a novel metric which relates the discrepancy between a known PSF and a choice of approximate PSF, and the resulting effect that this discrepancy will have on the reconstruction of an unblurred image. Such a metric is essential to the accurate development and application of a parameterized PSF model. Several error measures are proposed, which quantify the inaccuracy of image deblurring using a particular incorrect PSF. Using a set of simulation results, it is shown that the desired metric is feasible even without specification of the unblurred prior image or the radiometric response of the camera. It is also shown that the proposed metric accurately and reliably predicts the resulting deblurring error from the use of an approximate PSF in place of an exact PSF.