Extended object reconstruction in adaptive-optics imaging: the multiresolution approach," submitted to Astronomy & Astrophysics

Aims. We propose the application of multiresolution transforms, such as wavelets (WT) and curvelets (CT), to the reconstruction of images of extended objects that have been acquired with adaptive optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools in order to distinguish significant structures from noise and reconstruction residuals. Therefore, we also test the performance of two different probabilistic masks: one based on local correlation and the other on local standard deviation. Furthermore, we aim to check the historical assumption that image-reconstruction algorithms using static PSFs are not suitable for AO imaging. Methods. We convolve an image of Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and add both shot and readout noise. Subsequently, we apply different approaches to the blurred and noisy data in order to recover the original object. The approaches include multi-frame blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelets- or curvelets-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) and the structural similarity index (SSIM), also known as the Wang-Bovik index, to compare the results. We discuss the strengths and weaknesses of the two metrics and the usefulness of using more than one metric to evaluate the results of imaging restoration. Results. We found that CT produces better results than WT, as measured in terms of MSE and SSIM. In the wavelet domain, th