1. A method for filtering seismic data using one or more programmable computers programmed to at least perforin the operations of: receiving pressure data and velocity data generated by one or more multi-component sensors of one or more streamers towed by a survey vessel; initializing values of a filtered wavefield to zero; for a number of iterations, applying one or more filters to the pressure data and velocity data to generate a first filtered wavefield; applying singular value decomposition (“SVD”) to the first filtered wavefield to generate an extracted wavefield; updating the filtered wavefield based on the extracted wavefield to reduce noise in the filtered wavefield; applying SVD to the pressure data and the velocity data to generate corresponding extracted pressure data and extracted velocity data; adjusting the pressure and velocity data based on extracted pressure data and extracted velocity data; and storing the filtered wavefield in one or more computer-readable media.