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 sparse signals are quantized and expressed as bit sequences. By transforming l0-norm to a quadratic form of these bits, the quadratic objective function is provided to be optimized by the solver specialized for QUBO, such as the quantum annealer. Numerical experiments with a commercially available quantum annealer show the proposed method demonstrates the reconstruction success rate close to conventional methods based on the orthogonal matching pursuit (OMP) and the least absolute shrinkage and selection operator (LASSO).