This letter presents a novel quantum algorithm for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The proposed algorithm is able to process both classical and quantum signals. It is parametrically faster than previous classical and quantum denoising algorithms. Numerical results show that it is efficient at removing noise of both classical and quantum origin, significantly outperforming existing quantum algorithms in this respect, especially in the presence of quantum noise.