Sparse Signal Reconstruction: LASSO and Cardinality Approaches

The paper considers several optimization problem statements for signal sparse reconstruction problems. We tested performance of AORDA Portfolio Safeguard (PSG) package with different problem formulations. We solved several medium-size test problems with cardinality functions: (a) minimize L1-error of regression subject to a constraint on cardinality of the solution vector; (b) minimize cardinality of the solution vector subject to a constraint on L1-error of regression. We compared performance of PSG and IBM CPLEX solvers on these problems. Although cardinality formulations are very appealing because of the direct control of the number of nonzero variables, large problems are beyond the reach of the tested commercial solvers. Step-down from the cardinality formulations is the formulation with the constraint on the sum of absolute values of the solution vector. This constraint is a relaxation of the cardinality constraint. Medium and large problems (from SPARCO toolbox for testing sparse reconstruction algorithms) were solved with PSG in the following formulation: minimize L1-error subject to a constraint on the sum of absolute values of the solution vector. The further Nikita Boyko Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611 USA e-mail: [email protected] Gulver Karamemis Department of Information Systems and Operations Management, University of Florida, Gainesville, FL, 32611 USA e-mail: [email protected] Viktor Kuzmenko V.M. Glushkov Institute of Cybernetics, Kyiv, Ukraine e-mail: [email protected] Stan Uryasev Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611 USA e-mail: [email protected]