1. A method for producing a noise-reduced digital image captured using a digital imaging system having signal-dependent noise characteristics, comprising using a digital processor to perform at least some of the steps of: a) capturing one or more noisy digital images of a scene, wherein said at least one noisy digital image has signal-dependent noise characteristics; b) defining a functional relationship to relate the one or more noisy digital images to a noise-reduced digital image estimate, wherein the functional relationship includes at least two sets of unknown parameters, and wherein at least one of the sets of unknown parameters relates to the signal-dependent noise characteristics; c) defining an energy function responsive to the functional relationship which includes at least: i) a data fidelity term to enforce similarities between the one or more noisy digital images and the noise-reduced digital image estimate; and ii) a spatial fidelity term to encourage sharp edges in the noise-reduced digital image estimate; and d) using an optimization process to determine a noise-reduced image responsive to the energy function.