Coding techniques for oversampled steerable transforms

In this paper we study signal representation using oversampled steerable transforms. While in general it may not be efficient to use an oversampled representation for applications like compression, our work investigates efficient techniques for representing the oversampled data, given that after oversampling there exists substantial redundancy. We discuss different strategies which take advantage of this oversampling by establishing some consistency constraints on the representation that reduce uncertainty in the quantization. This results in a coding gain as we increase the oversampling in the steerable transform (number of orientations). Thus, while in general it will not be possible to achieve as good compression performance as with a critically sampled transform, having a compressed steerable representation will be useful for applications where a feature is needed (many significant image features can be extracted from an orientation analysis), and where for performance reasons it is preferable not to have to decompress and analyze each image (as may be necessary if standard non-steerable transforms are used for compression).