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We introduce an algorithm for the deconvolution of radio synthesis imagesthat accounts for the non-coplanar-baseline effect, allows multiscalereconstruction onto arbitrarily positioned pixel grids, and allows the antennaelements to have direcitonal dependent gains. Using numerical L1-minimisationtechniques established in the application of compressive sensing to radioastronomy, we directly solve the deconvolution equation using GPU (graphicsprocessing unit) hardware. This approach relies on an analytic expression forthe contribution of a pixel in the image to the observed visibilities, and thewell-known expression for Dirac delta function pixels is used along with twonew approximations for Gaussian pixels, which allow for multi-scaledeconvolution. The algorithm is similar to the CLEAN algorithm in that it fitsthe reconstructed pixels in the image to the observed visibilities whileminimising the total flux; however, unlike CLEAN, it operates on the ungriddedvisibilities, enforces positivity, and has guaranteed global convergence. Thepixels in the image can be arbitrarily distributed and arbitrary gains betweeneach pixel and each antenna element can also be specified. Direct deconvolutionof the observed visibilities is shown to be feasible for several deconvolutionproblems, including a 1 megapixel wide-field image with over 400,000visibilities. Correctness of the algorithm is shown using synthetic data, andthe algorithm shows good image reconstruction performance. Though thisalgorithm requires significantly more computation than methods based on theCLEAN algorithm, we demonstrate that it is trivially parallelisable acrossmultiple GPUs and potentially can be scaled to GPU clusters. We alsodemonstrate that a significant speed up is possible through the use ofmulti-scale analysis using Gaussian pixels.

Direct deconvolution of radio synthesis images using L1 minimisation