Real-time sparse signal reconstruction via KKT-conditions-driven analog circuit solver

In engineering and scientific fields, solving efficiency of sparse signal reconstruction problem is placed extremely high demands on. Numerical-based methods are confronted with the dilemma of exponential growth in computational complexity as the dimensionality and structural complexity of problems increase. To address the challenge and obtain real-time solution, an analog circuit solver based on KKT conditions is proposed for the sparse signal reconstruction. For the two typical reconstruction scenarios of noiseless and noisy cases, the Basis Pursuit (BP) problem is transformed into a linear programming (LP) problem and the Basis Pursuit DeNoising (BPDN) problem into a quadratic programming (QP) problem, respectively. Based on the KKT conditions of the considered problems, together with Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL), and Ohm's law, we design dedicated circuit modules to construct various analog circuit topologies. This realizes the accurate mapping from theoretical optimization problems to physical circuit implementations. Without capacitors integrating device, the analog solver proposed could gain real-time solution. Furthermore, this paper deeply explains the underlying physical mechanism in which circuits embedded with nonreciprocal components obey the stationary cocontent theorem. Employing Multisim simulation platform, we conducted some comparative simulation experiments, and the presented approach is compared with other numerical methods, such as classical discrete and continuous algorithms. This not only verifies the effectiveness of the method, but also highlights its core advantage-real-time performance.