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PURIFY is a collection of routines written in C that implements different tools for radio-interferometric imaging including file handling (for both visibilities and fits files), implementation of the measurement operator and set-up of the different optimization problems used for image deconvolution. The code calls the generic Sparse OPTimization (SOPT) package to solve the imaging optimization problems.
SOPT (Sparse OPTimisation) is a C implementation of the Sparsity Averaging Reweighted Analysis (SARA) algorithm. The approach relies on the observation that natural images exhibit strong average sparsity; average sparsity outperforms state-of-the-art priors that promote sparsity in a single orthonormal basis or redundant frame, or that promote gradient sparsity.
Fourierdimredn (Fourier dimensionality reduction) implements Fourier-based dimensionality reduction of interferometric data. Written in Matlab, it derives the theoretically optimal dimensionality reduction operator from a singular value decomposition perspective of the measurement operator. Fourierdimredn ensures a fast implementation of the full measurement operator and also preserves the i.i.d. Gaussian properties of the original measurement noise.
SARA-PPD is a proof of concept MATLAB implementation of an acceleration strategy for a recently proposed primal-dual distributed algorithm. The algorithm optimizes resolution by accounting for the correct noise statistics, leverages natural weighting in the definition of the minimization problem for image reconstruction, and optimizes sensitivity by enabling accelerated convergence through a preconditioning strategy incorporating sampling density information. This algorithm offers efficient processing of large-scale data sets that will be acquired by next generation radio-interferometers such as the Square Kilometer Array.
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible, creating an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging, leading to an alternated minimization problem; in that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss–Seidel method.
The Optical-Interferometry-Trilinear code improves the approach on three fundamental aspects. First, the estimated image is defined as a solution of a regularized minimization problem, promoting sparsity in a fixed dictionary using either an l1 or a (re)weighted-l1 regularization term. Second, the resultant non-convex minimization problem is solved using a block-coordinate forward–backward algorithm. This algorithm is able to deal both with smooth and non-smooth functions, and benefits from convergence guarantees even in a non-convex context. Finally, the model and algorithm are generalized to the hyperspectral case, promoting a joint sparsity prior through an l2,1 regularization term.