This paper focusses on safe screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed joint screening test, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respectively expressed as sphere and dome regions. After presenting the mathematical derivations of the tests, we elaborate on their relative effectiveness and discuss the practical use of such procedures.
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