Solar hard X-ray imaging by means of compressed sensing and finite isotropic wavelet transform

Aims. Compressed sensing realized by means of regularized deconvolution and the finite isotropic wavelet transform is effective and reliable in hard X-ray solar imaging. Methods. The method uses the finite isotropic wavelet transform with the Meyer function as the mother wavelet. Furthermore, compressed sensing is realized by optimizing a sparsity-promoting regularized objective function by means of the fast iterative shrinkagethresholding algorithm. Eventually, the regularization parameter is selected by means of the Miller criterion. Results. The method is applied against both synthetic data mimicking measurements made with the Spectrometer/Telescope Imaging X-rays (STIX) and experimental observations provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The performances of the method are qualitatively validated by comparing some morphological properties of the reconstructed sources with those of the corresponding synthetic configurations. Furthermore, the results concerning experimental data are compared with those obtained by applying other visibility-based reconstruction methods. Conclusions. The results show that when the new method is applied to synthetic STIX visibility sets, it provides reconstructions with a spatial accuracy comparable to the accuracy provided by the most popular method in hard X-ray solar imaging and with a higher spatial resolution. Furthermore, when it is applied to experimental RHESSI data, the reconstructions are characterized by reliable photometry and by a notable reduction of the ringing effects caused by the instrument point spread function.