A multiscale hybrid linear model for lossy image representation

This paper introduces a simple and efficient representation for natural images. We partition an image into blocks and treat the blocks as vectors in a high-dimensional space. We then fit a piecewise linear model (i.e. a union of affine subspaces) to the vectors at each down-sampling scale. We call this a multiscale hybrid linear model of the image. The hybrid and hierarchical structure of this model allows us effectively to extract and exploit multimodal correlations among the imagery data at different scales. It conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation (e.g. DCT, wavelets), an adaptive unimodal linear transformation (e.g. PCA), or a multi-modal model at a single scale. We will justify both analytically and experimentally why and how such a simple multiscale hybrid model is able to reduce simultaneously the model complexity and computational cost. Despite a small overhead for the model, our results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal-to-noise ratio than many existing methods, including wavelets.