Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation

Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors). In this article, a series of strategies to visualise this uncertainty are presented, e.g. highest posterior density credible regions, and local credible intervals (cf. error bars) for individual pixels and superpixels. Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings. Moreover, we present strategies to automatically set regularisation parameters so that the proposed uncertainty quantification (UQ) strategies become much easier to use. Also, different kinds of dictionaries (complete and over-complete) are used to represent the image/signal and their performance in the proposed UQ methodology is investigated.Comment: 5 pages, 5 figure

A fast and exact ww-stacking and ww-projection hybrid algorithm for wide-field interferometric imaging

The standard wide-field imaging technique, the $w$-projection, allows correction for wide-fields of view for non-coplanar radio interferometric arrays. However, calculating exact corrections for each measurement has not been possible due to the amount of computation required at high resolution and with the large number of visibilities from current interferometers. The required accuracy and computational cost of these corrections is one of the largest unsolved challenges facing next generation radio interferometers such as the Square Kilometre Array. We show that the same calculation can be performed with a radially symmetric $w$-projection kernel, where we use one dimensional adaptive quadrature to calculate the resulting Hankel transform, decreasing the computation required for kernel generation by several orders of magnitude, whilst preserving the accuracy. We confirm that the radial $w$-projection kernel is accurate to approximately 1% by imaging the zero-spacing with an added $w$-term. We demonstrate the potential of our radially symmetric $w$-projection kernel via sparse image reconstruction, using the software package PURIFY. We develop a distributed $w$-stacking and $w$-projection hybrid algorithm. We apply this algorithm to individually correct for non-coplanar effects in 17.5 million visibilities over a $25$ by $25$ degree field of view MWA observation for image reconstruction. Such a level of accuracy and scalability is not possible with standard $w$-projection kernel generation methods. This demonstrates that we can scale to a large number of measurements with large image sizes whilst still maintaining both speed and accuracy.Comment: 9 Figures, 19 Pages. Accepted to Ap

Célia Bertin: Jean Renoir – A Life in Pictures

RECENTLY, the scholarly Alistair Cooke was introducing John Mortimer's Renoir reminiscent tv-film series, Summer Lease on PBS. In describing the origins of the story, which lay in the author's family visits to Italy, Cooke started a train of thought on the number of artists over the years whose work was inspired by their parents' activities, family relations, the tales they heard as children, the travels they took and the institutions they attended, all forming an important part of their growing years and providing them with a vivid background to draw upon in their creative periods which followed. Co-incidentally, a new biography of the distinguished French filmmaker, Jean Renoir, the son the greatest painter of the time, provides us with a detailed and colourful description of how deeply influenced Jean was by his father, Auguste and family; and how much his films reflected this without in anyway detracting from Jean..

The Future of Two Festivals

BERLIN 1992 Flying into Berlin is now so very ordinary. No need to worry about wandering out of the narrow corridor over East Germany leading into the divided city; no fear now of being shot down by a watchful MIG; now the Frankfurt-Berlin train can stop where it likes and motorists can leave the autobahn on the way in. The fear and atmosphere of menace have gone. Checkpoint Charlie has gone; Bernard Samson has come out for the last time. No one will get riddled with bullets trying to cross the Wall because the Wall has disappeared. Was it ever there? Hard to believe as the West Berlin double-deckers pass the Brandenburg Gate and drive straight through to Alexanderplatz. A history of forty years has disappeared, to become a tick in time a hundred years hence. Surprisingly many former West Berliners are not too happy about this sudden..