Framed Frames For Data Frames

We present a computationally efficient, data-driven procedure for constructing linear isometric embeddings of high-dimensional data (data frames) into spaces of smooth images, and thereby obtain tight frame dictionaries for the data space using tight frame dictionaries for the image space ("framed frames" - wavelets, curvelets, shearlets, etc.). Experiments indicate that data are more compressible in these induced dictionaries when compared to compressibility in terms of principal components.