The factored-SVD formulation and an application example

Recent work has shown how the singular value decomposition (SVD) may be used in a multiresolution form analogous to the wavelet decomposition. Here it will be shown how a particular realization of the multiresolution SVD (MR-SVD) yields a decomposition into Kronecker products which enables efficient synthesis of the original signal. Furthermore, it is demonstrated that the resulting decomposition (called the factored-SVD), when applied in similar fashion to a wavelet packet decomposition, provides a significant reduction in distortion over the well-known Karhunen–Loeve transform (KLT) as a result of rate-distortion coding in a higher dimensionality space. Application to the 512×512 Lena image indicates SNR improvements of almost 20 dB, which are in agreement with the theoretical development. Finally, other future applications are suggested.