Code and Data supplement to

Astrophysicists are interested in recovering the 3D gas emissivity of a galaxy cluster from a 2D image taken by a telescope. A blurring phenomenon and presence of point sources make this inverse problem even harder to solve. The current state-of-the-art technique is two step: First identify the location of potential point sources, then mask these locations and deproject the data.

We instead model the data as a Poisson generalized linear model (involving blurring, Abel and wavelets operators) regularized by two lasso penalties to induce sparse wavelet representation and sparse point sources. The amount of sparsity is controlled by two quantile universal thresholds. As a result, our method outperforms the existing one.

Requirements

• Download and extract ASTROQUT. Available here.
• Add folders 'ASTROQUT/FISTA', 'ASTROQUT/simfunc' and 'ASTROQUT/code' to MATLAB path.
• Download and Install WAVELAB 850. Available here.
• Compile 'deprojection.C' in your own Operative System. This file is in the root of ASTROQUT, it allows to do the inversion using the state-of-the-art techinique. You will need a C compiler.
• ASTROQUT is implemented in MATLAB.

• To run all simulations in the paper, go to the root folder 'ASTROQUT' in MATLAB and run 'reproduceALL'. By default it runs using parallel computations, you can change that by setting options.parallel=0 and replacing 'parfor' by 'for', in all simulation files.
• To denoise an image: 'astrosolveWS.m'.
• To simulate and denoise an image: 'astrosimPS.m'.
• To denoise an image and get pointwise confidence interval by bootstrap: 'astrobootWS.m'.

Folder 'data_and_results' includes chandra ('FEOchandra.mat') and XMM ('FEOxmm.mat') datasets. F is the image, E is the sensitivity and O is the Offset.