In this work, we propose a new symbol detection method in faster-than-Nyquist signaling for effective data transmission. Based on the frame theory, the symbol detection problem is described as under-determined linear equations on a finite alphabet. While the problem is itself NP (non-deterministic polynomial-time) hard, we propose convex relaxation using the sum-of-absolute-values optimization, which can be efficiently solved by proximal splitting. Simulation results are shown to illustrate the effectiveness of the proposed method compared to a recent ell-infinity-based method.