Image reconstruction and restoration in astronomy

Since the discovery of the spherical aberration problem in the Hubble Space Telescope in 1990, a substantial amount of work has been done in image reconstruction and restoration directed toward optical astronomy. We refer to image restoration when the raw data is “imagelike,” while in the case of image reconstruction we attempt to construct the image from raw data that do not resemble an image at all. However, the image reconstruction and the image restoration problems have the same mathematical formulation. Both are particular cases of the ill-posed inverse problem. Image restoration is important for astronomy from the ultraviolet to the infrared, not only to improve the visual quality of the images but also to increase the scientific content and to obtain super-resolution beyond the diffraction limit. Image reconstruction is of fundamental importance in several astronomical fields such as radioastronomy (interferometry), space astronomy (X-ray, y-ray) etc. Outside astronomy, the inverse problem appears in fields as diverse as medical tomography, nuclear magnetic resonance, molecular biology, acoustics, seismology, interferometry, spectroscopy, signal processing, radar imaging, and echography. During the 1960s and 1970s, a considerable amount of research on image restoration was performed, as can be seen in the book by Andrews and Hunt [l]. From this period came studies such as the papers of Richardson [2] and Lucy [3] and the development of the Maximum Entropy Method. However, during the 1980s little was added to the topic of image restoration. Fortunately, at the same time there was a great burst of activity in other fields such as medical imaging with studies such as the paper of Shepp and Vardi [4] on maximum likelihood image reconstruction for emission tomography. Thanks to the wide applicability of the research on inverse problem, it was relatively easy to apply the developments in medical imaging to image reconstruction / restoration in astronomy. AS stated previously, the discovery of the imperfect optics of the Hubble Space Telescope focused an important effort on the image restoration problem in the 1990s, which led to two important conferences on image restoration in 1990 [5] and 1993 [6], both held at the Space Telescope Science Institute in Baltimore, Maryland. Since the last Baltimore conference in 1993, the efforts in this field have not stopped, but have continued intensively. The purpose of this special issue is to present the state of the art in the field of image reconstruction/restoration in astronomy. We hope that this special issue could be considered the third in the series initiated by the proceedings of the Baltimore meetings. While no collection can cover all aspects, the articles included here cover many important directions. Some of the articles introduce new theoretical developments in the control of the inversion process, while others describe new results and applications. One of the fundamental applications of image reconstruction is to achieve super-resolution. The basic motivations for super-resolution, the reasons why it can be made to work, the algorithms, and its expected performance are presented by B. R. Hunt in “Super-resolution of images: Algorithms, principles, performance.” The control of noise amplification is the key problem in any ill-posed inverse problem. In “Spatially adaptive iterative algorithm for the restoration of astronomical images,” A. K. Katsaggelos et al. develop a regularized image restoration algorithm that is adaptive in space. Another possibility to control noise amplification is to use multirresolution techniques. These are developed in two articles. R. C. Puetter in “Pixon-based multiresolution image reconstruction and the quantification of picture information content” reviews pixon-based image reconstruction, while F. Murtagh et al. in “Multiresolution in astronomical image processing: A general framework” use the wavelet and pyramidal median transforms. For obvious reasons, the most active centers in image restoration in the last years were the Space Telescope Institutes. The intense work done at the Space Telescope-European Coordinating Facility on the implementation and extensions of the Richardson-Lucy and other algorithms is described by H.M. Adorf et al. in the article “HST image restoration developments at the ST-ECF.” Artificial neural networks is a very versatile tool to solve a large number of problems. In “Convolution connection paradigm neural network enables linear system theory-based image enhancement,” W. E. Blass et al. use the neural networks to obtain a numeric solution of the deconvolution problem. One principle is widely used in physics: Occam’s principle of maximum simplicity of model in data interpretation. V. Yu. Terebizh, in “Occamian approach in image restoration and