The discrete modal transform and its application to lossy image compression

摘要

This paper introduces the discrete modal transform (DMT), a 1D and 2D discrete, non-separable transform for signal processing, which, in the mathematical sense, is a generalization of the well-known discrete cosine transform (DCT). A 3D deformable surface model is used to represent the image intensity and the introduced discrete transform is a by-product of the explicit surface deformation governing equations. The properties of the proposed transform are similar to those of the DCT. To illustrate these properties, the proposed transform is applied to lossy image compression and the obtained results are compared to those of a DCT-based compression scheme. Experimental results show that DMT, which includes an embedded compression ratio selection mechanism, has excellent energy compaction properties and achieves comparable compression results to DCT at low compression ratios, while being in general better than DCT at high compression ratios.