STARRED: a two-channel deconvolution method with Starlet regularization

Abstract

The spatial resolution of astronomical images is limited by atmospheric turbulence and diffraction in the telescope optics, resulting in blurred images. This makes it difficult to accurately measure the brightness of blended objects because the contributions from adjacent objects are mixed in a time-variable manner due to changes in the atmospheric conditions. However, this effect can be corrected by characterizing the Point Spread Function (PSF), which describes how a point source is blurred on a detector. This function can be estimated from the stars in the field of view, which provides a natural sampling of the PSF across the entire field of view. Once the PSF is estimated, it can be removed from the data through the so-called deconvolution process, leading to images of improved spatial resolution. The deconvolution operation is an ill-posed inverse problem due to noise and pixelization of the data. To solve this problem, regularization is necessary to guarantee the robustness of the solution. Regularization can take the form of a sparse prior, meaning that the recovered solution can be represented with only a few basis eigenvectors. STARRED is a Python package developed in the context of the COSMOGRAIL collaboration and applies to a vast variety of astronomical problems. It proposes to use an isotropic wavelet basis, called Starlets, to regularize the solution of the deconvolution problem. This family of wavelets has been shown to be well-suited to represent astronomical objects. STARRED provides two modules to first reconstruct the PSF, and then perform the deconvolution. It is based on two key concepts: i) the image is reconstructed in two separate channels, one for the point sources and one for the extended sources, and ii) the code relies on the deliberate choice of not completely removing the effect of the PSF, but rather bringing the image to a higher resolution.

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