Our research focuses on testing the robustness of Quantum Signal Processing (QSP) against a wide range of noise models and developing frameworks for algorithmic-level error correction. Using an in-house stable Prony-based factorization method, we generate high-precision QSP phase factors for challenging quantum algorithms without the numerical instabilities of traditional root-finding approaches. We then evaluate how these sequences perform under systematic and stochastic errors, including multiplicative over/under-rotations, and design “recovery QSP” sequences—built entirely from the same noisy operations, that cancel dominant error components to arbitrary order without additional quantum resources. This combined approach advances both the precision of QSP and its resilience to realistic hardware imperfections, paving the way for scalable, noise-robust quantum algorithms.