Linear inverse problems such as signal decomposition and reconstruction are crucial issues for fault diagnosis in mechanical equipment. In this paper, we propose a novel class of non-convex penalty defined via generalized infimal convolution smoothing (GICS). As a multivariate generation of logarithm function, it can guarantee global convexity of the overall objective function. Combining wavelet transform, sparse representation and optimization algorithm, extracting signal components from observed signal submerged in strong noise is possible. Simulated case and practical signal measured from gearbox demonstrate improvements upon L1 norm convex penalty and a newly developed non-convex regularizer called generalized minimax-concave (GMC).