Sparse Signal Reconstruction with QUBO Formulation in l0-regularized Linear Regression

An l0-regularized linear regression for a sparse signal reconstruction is implemented based on the quadratic unconstrained binary optimization (QUBO) formulation. In this method, the signal values are quantized and expressed as bit sequences. By transforming l0-norm to a quadratic form of these bits, the fully quadratic objective function is provided and optimized by the solver specialized for QUBO, such as the quantum annealer. Numerical experiments with a commercial quantum annealer show that the proposed method performs slightly better than conventional methods based on orthogonal matching pursuit (OMP) and the least absolute shrinkage and selection operator (LASSO) under several limited conditions.