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This paper describes a new efficient conjugate subgradient algorithm whichminimizes a convex function containing a least squares fidelity term and anabsolute value regularization term. This method is successfully applied to theinversion of ill-conditioned linear problems, in particular for computedtomography with the dictionary learning method. A comparison with otherstate-of-art methods shows a significant reduction of the number of iterations,which makes this algorithm appealing for practical use.

A conjugate subgradient algorithm with adaptive preconditioning for LASSO minimization