Multi-Scale CLEAN deconvolution of radio synthesis images

Radio synthesis imaging is dependent upon deconvolution algorithms to counteract the sparse sampling of the Fourier plane. These deconvolution algorithms find an estimate of the true sky brightness from the necessarily incomplete sampled visibility data. The most widely used radio synthesis deconvolution method is the CLEAN algorithm of Hogbom. This algorithm works extremely well for collections of point sources and surprisingly well for extended objects. However, the performance for extended objects can be improved by adopting a multi-scale approach. We describe and demonstrate a conceptually simple and algorithmically straightforward extension to CLEAN that models the sky brightness by the summation of components of emission having different size scales. While previous multiscale algorithms work sequentially on decreasing scale sizes, our algorithm works simultaneously on a range of specified scales. Applications to both real and simulated data sets are given.Comment: Submitted to IEEE Special Issue on Signal Processin

PURIFY: a new approach to radio-interferometric imaging

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a minimization problem for image reconstruction. This approach was shown, in theory and through simulations in a simple discrete visibility setting, to have the potential to outperform significantly CLEAN and its evolutions. In this work, we leverage the versatility of convex optimization in solving minimization problems to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted relies on the simultaneous-direction method of multipliers (SDMM), and contrasts with the current major-minor cycle structure of CLEAN and its evolutions, which in particular cannot handle the state-of-the-art minimization problems under consideration where neither the regularization term nor the data term are differentiable functions. We release a beta version of an SDMM-based imaging software written in C and dubbed PURIFY (http://basp-group.github.io/purify/) that handles various sparsity priors, including our recent average sparsity approach SARA. We evaluate the performance of different priors through simulations in the continuous visibility setting, confirming the superiority of SARA

Tailoring laser pulses with spectral and fluence constraints using optimal control theory

Within the framework of optimal control theory we develop a simple iterative scheme to determine optimal laser pulses with spectral and fluence constraints. The algorithm is applied to a one-dimensional asymmetric double well where the control target is to transfer a particle from the ground state, located in the left well, to the first excited state, located in the right well. Extremely high occupations of the first excited state are obtained for a variety of spectral and/or energetic constraints. Even for the extreme case where no resonance frequency is allowed in the pulse the algorithm achieves an occupation of almost 100%