1. A method of processing a multi-dimensional signal composed of a collection of arbitrarily shaped domains via a multi-scale transform comprising the steps of: a. Obtaining a multi-dimensional digital image frame; b. Breaking the image frame into constituent arbitrary shaped domains, or given such a set, that cover all or a portion of the original multidimensional signal domain; and c. Performing a combined domain and pattern adaptive transform on one or more of the collection of arbitrary shaped domains, wherein the combined domain and pattern adaptive transform comprises a domain adaptive transform followed by a pattern adaptive transform, wherein a filter comprising a convolution operator is applied to process pixels near a boundary of the domain, and wherein filter coefficients for an interpolation filter are scaled by an inverse of a gradient value.