Ayaka Sakata

Perfect reconstruction of sparse signals with piecewise continuous nonconvex penalties and nonconvexity control

We explore the use of nonconvex penalties, specifically Smoothly Clipped Absolute Deviations (SCAD) and Minimax Concave Penalties (MCP), which offer continuity, unbiasedness, and sparsity to estimators. Our study verifies their superior performance compared to L1 minimization, achieving perfect reconstruction with fewer measurements. We employ the Approximate Message Passing (AMP) algorithm but find a discrepancy between theory and practice. To address this, we introduce nonconvexity control, improving AMP's performance. Our findings demonstrate the potential of nonconvex penalties for efficient and accurate signal reconstruction in compressed sensing.