1. A method for processing a single-channel input including speech and noise, comprising: receiving, by a processor, the single-channel input captured via a microphone; for processing a current frame of the single-channel input: performing, by the processor, a time-frequency transformation on the single-channel input over L frames including the current frame to obtain an extended observation vector of the current frame, data elements in the extended observation vector representing coefficients of the time-frequency transformation of the L frames of the single-channel input; computing, by the processor, second-order statistics of the extended observation vector; if the current frame of the single-channel input does not include detectable human voice activity, computing, by the processor, second-order statistics of noise contained in the single-channel input; constructing, by the processor, a noise reduction filter for the current frame of the single-channel input based on the second-order statistics of the extended observation vector and the second-order statistics of noise; and applying the noise reduction filter to the single-channel input to reduce an amount of noise; wherein L>1.