Joint imaging and calibration using non-convex optimization.

A. Repetti and Y. Wiaux.

Workshop on Variational methods, new optimisation techniques and new fast numerical algorithms , Isaac Newton Institute, Cambridge, UK, 4-8 Sept. 2017.

New generations of imaging devices aim to produce high resolution and high dynamic range images. In this context, the high dimensionality associated inverse problems can become extremely challenging from an algorithmic view point. In addition, the quality and accuracy of the reconstructed images often depend on the precision with which the imaging device has previously been calibrated. Unfortunately, calibration does not depend only on the device but may also rely on the time and on the direction of the acquisitions. This leads to the need of performing joint image reconstruction and calibration, and thus of solving non-convex blind deconvolution problems. We focus on the joint calibration and imaging problem in the context of radio-interferometric imaging in astronomy. In this case, the sparse images of interest can reach gigapixel or terapixel size, while the calibration variables consist of a large number of low resolution images related to each antenna of the telescope. To solve this problem, we leverage a block-coordinate forward-backward algorithm, specifically designed to minimize non-smooth non-convex and high dimensional objective functions. We demonstrate by simulation the performance of this first joint imaging and calibration method in radio-astronomy.




Biomedical and Astronomical Signal Processing group
Institute of Sensors, Signals and Systems
Heriot-Watt University
Edinburgh EH14 4AS

mail: A.Repetti@hw.ac.uk