Signal restoration involves the removal or minimization of degradation such as attenuation, interference, and noise. Blind signal restoration is the process of estimating either the original signals or mixture functions from the degraded signals, without any prior information about original sources. In this paper, we present a novel approach to tackle the ill-posedness of the nonlinear blind source separation problem. The derivation of our algorithm is inspired by the idea of an efficient layer-by-layer representation to approximate the nonlinearity. Once such representations are built, a final output layer is constructed by solving a convex optimization problem. Thus, the projected data can break a nonlinear problem down into the version of generalized joint diagonalization problem in the feature space. Importantly, the parameters and forms of polynomials depend solely on the input data, which guarantee the robustness of the structure. We thus address the general problem without being restricted to any specific mixture or parametric model. Experimental results show that the proposed algorithm is able to recover the nonlinear mixture with higher separation accuracy on audio datasets from the real world.