Classical single channel restoration attempts to remove or reduce the blurring of an image which results from its convolution with an instrumental or atmospheric point-spread function (PSF). The topic was extensively discussed following the discovery of spherical aberration in images from the Hubble Space Telescope in summer 1990. It was quickly found that such methods could certainly improve the contrast and apparent sharpness of images to some extent but that such improvements were tightly constrained by the noise characteristics of the data, knowledge of the PSF as well as the presence of artifacts. At this stage the Richardson-Lucy (RL, Richardson 1972, Lucy 1974) method was widely adopted as it is a formally correct maximum likelihood algorithm for images with Poissonian (and hence non-negative) noise characteristics. Lucy has investigated in detail the true gain in resolution which is possible from restoration methods on test images having differing signal to noise ratios (Lucy 1992). This study reveals that resolution gains of greater than 2, or possibly 3, are possible for high signal to noise images but that higher resolution enhancements require data with s/n ratios which are impossible to achieve in practice.
Methods such as RL are iterative and non-linear. As iterations proceed the result gets sharper but after a while the method overfits the noise. It becomes an important question to determine the number of iterations to apply for optimum results and unfortunately the answer to this question varies within the image - high signal-to-noise ratio areas (for example the bright nuclear region of a galaxy) require more iterations than the faint and noisy background. The non-linearity leads to many kinds of artifacts as well as highly correlated noise. It is hence much more difficult to decide whether or not a feature in a restored image is real using simple statistical tests than for an image with known pixel-to-pixel noise characteristics.
In order to reduce the computational requirements of RL, which can be demanding for large images, several acceleration schemes have been proposed (eg, Hook & Lucy, 1993b). These are implemented in both the acoadd and the lucy tasks in STSDAS.
More complex methods such as those using entropy constraints as well as likelihood maximisation have proved quite successful in many fields. They have the advantage over RL that stopping rules do not have to be so arbitrary and control of the resolution to be attempted is possible. Another very powerful approach is the `pixon' method (Dixon et al. 1996) which overcomes the problem that different parts of the image contain different amounts of information by only allowing the result to contain a level of detail which is statistically justified by the data.