Methods for representing multiple scales in an image using a variational algorithm are provided. An iterative decomposition of an image into a total variation (“TV”) part, which may be a weighted TV (“TVα”) part, and a residual part motivates the design and use of a partial differential equation that may be referred to as a multiscale total variation flow, or multiscale weighted total variation flow. This produces a multiscale representation of the image. The speed of this decomposition can be controlled with a user-defined function, and is fast enough to allow for real-time applications of denoising and image registration.
