Deconvolution of astronomical images using SOR with adaptive relaxation.

We address the potential performance of the successive overrelaxation technique (SOR) in image deconvolution, focusing our attention on the restoration of astronomical images distorted by atmospheric turbulence. SOR is the classical Gauss-Seidel iteration, supplemented with relaxation. As indicated by earlier work, the convergence properties of SOR, and its ultimate performance in the deconvolution of blurred and noisy images, can be made competitive to other iterative techniques, including conjugate gradients, by a proper choice of the relaxation parameter. The question of how to choose the relaxation parameter, however, remained open, and in the practical work one had to rely on experimentation. In this paper, using constructive (rather than exact) arguments, we suggest a simple strategy for choosing the relaxation parameter and for updating its value in consecutive iterations to optimize the performance of the SOR algorithm (and its positivity-constrained version, +SOR) at finite iteration counts. We suggest an extension of the algorithm to the notoriously difficult problem of "blind" deconvolution, where both the true object and the point-spread function have to be recovered from the blurred image. We report the results of numerical inversions with artificial and real data, where the algorithm is compared with techniques based on conjugate gradients. In all of our experiments +SOR provides the highest quality results. In addition +SOR is found to be able to detect moderately small changes in the true object between separate data frames: an important quality for multi-frame blind deconvolution where stationarity of the object is a necesessity.

Helioseismic measurement of solar torsional oscillations.

Bands of slower and faster rotation, the so-called torsional oscillations, are observed at the Sun's surface to migrate in latitude over the 11-year solar cycle. Here, we report on the temporal variations of the Sun's internal rotation from solar p-mode frequencies obtained over nearly 6 years by the Michelson Doppler Imager (MDI) instrument on board the Solar and Heliospheric Observatory (SOHO) satellite. The entire solar convective envelope appears to be involved in the torsional oscillations, with phase propagating poleward and equatorward from midlatitudes at all depths throughout the convective envelope.