Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain