Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image regularization. Contrarily to most methods presented in the literature, our method does not assume a parametric model of the PSF and can thus be applied to any telescope. Methods: Our scheme uses a wavelet analysis prior model on the image and weak assumptions on the PSF. We use observations from a celestial transit, where the occulting body can be assumed to be a black disk. These constraints allow us to retain meaningful solutions for the filter and the image, eliminating trivial, translated, and interchanged solutions. Under an additive Gaussian noise assumption, they also enforce noise canceling and avoid reconstruction artifacts by promoting the whiteness of the residual between the blurred observations and the cleaned data. Results: Our method is applied to synthetic and experimental data. The PSF is estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for SDO/AIA using the 2012 Venus transit. Results show that the proposed non-parametric blind deconvolution method is able to estimate the core of the PSF with a similar quality to parametric methods proposed in the literature. We also show that, if these parametric estimations are incorporated in the acquisition model, the resulting PSF outperforms both the parametric and non-parametric methods.
The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo 2π observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by recording complex or modulated data from which a "wrapped" phase is extracted. Although 1-D phase unwrapping is trivial, a challenge remains in higher dimensions to overcome two common problems: noise and discontinuities in the true phase image. In contrast to state-of-the-art techniques, this work aims at simultaneously unwrap and denoise the phase image. We propose a robust convex optimization approach that enforces data fidelity constraints expressed in the corrupted phase derivative domain while promoting a sparse phase prior. The resulting optimization problem is solved by the Chambolle-Pock primal-dual scheme. We show that under different observation noise levels, our approach compares favorably to those that perform the unwrapping and denoising in two separate steps.
We consider the problem of reconstructing an image from compressive measurements using a multi-resolution grid. In this context, the reconstructed image is divided into multiple regions, each one with a different resolution. This problem arises in situations where the image to reconstruct contains a certain region of interest (RoI) that is more important than the rest. Through a theoretical analysis and simulation experiments we show that the multi-resolution reconstruction provides a higher quality of the RoI compared to the traditional single-resolution approach.
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