The problem presented by the blurred images obtained from the Hubble Space Telescope is a common one throughout science. Given a digital signal degraded by (approximately) stationary blurring and an estimate of the point spread function defining the blur, we seek to recover an improved approximation to the unblurred signal. Such blurs occur in 1-D chemical spectra and 2-D and 3-D images from microscopes, telescopes, photographs, CT and MRI scanners, satellite sensors, and scintigrams (nuclear medicine images). Lucy (1974) lists a series of problems in astronomy that depend on the ability to remove blur from image or spectral measurements. Jansson and his associates (1968, 1970a, 1970b) have studied extensively the problem of removing or characterizing the blurring function of spectrographs.
The same basic iterative deconvolution algorithm has been independently developed in astronomy and medical image processing and has migrated from those fields to many others. This iterative algorithm is highly sensitive to image noise and to errors in the estimate of the point spread function. Similar modifications to the basic algorithm have been proposed in both fields. One common modification involves introducing a nonlinear relaxation factor into the algorithm to accelerate convergence and suppress noise, but then image flux is no longer conserved. Thus, in astronomy for example, the deblurred image is no longer suitable for photometry since nonlinear, spatially varying changes in intensity are produced by the modified deblurring procedures.
This paper introduces a new iterative and recursive deconvolution procedure that is flux-conserving, linear, and relatively insensitive to noise or to error in the estimate of the point spread function. Results of a mathematical analysis of the iterative/recursive method will be presented, and a demonstration of the algorithm will be presented based on the blurring function of the Hubble Space Telescope.