Extended-object reconstruction in adaptive-optics imaging: The multiresolution approach

Aims. We propose the application of multiresolution transforms, such as wavelets and curvelets, to reconstruct images of extended objects that have been acquired with adaptive-optics (AO) systems. Such multichannel approaches normally make use of probabilistic tools to distinguish significant structures from noise and reconstruction residuals. We aim to check the prevailing assumption that image-reconstruction algorithms using static point spread functions (PSF) are not suitable for AO imaging. Methods. We convolved two images, one of Saturn and one of galaxy M100, taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m Hale telescope at the Palomar Observatory and added shot and readout noise. Subsequently, we applied different approaches to the blurred and noisy data to recover the original object. The approaches included multiframe blind deconvolution (with the algorithm IDAC), myopic deconvolution with regularization (with MISTRAL) and wavelet- or curvelet-based static PSF deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error (MSE) to compare the results. Results. We found that multichannel deconvolution with a static PSF produces generally better results than the results obtained with the myopic/blind approaches (for the images we tested), thus showing that the ability of a method to suppress the noise and track the underlying iterative process is just as critical as the capability of the myopic/blind approaches to update the PSF. Furthermore, for these images, the curvelet transform (CT) produces better results than the wavelet transform (WT), as measured in terms of MSE.