Eigenvalue approach to analysis of performance of non-orthogonal perfect reconstruction filter banks in signal reconstruction applications

In the paper, a new approach to gain deeper insight into the performance of non-orthogonal (biorthogonal) perfect reconstruction filter banks in signal reconstruction applications is proposed. It is shown that signal reconstruction applications can utilize the potential of modification of signal-to-additive-signal ratio of non-orthogonal perfect reconstruction filter banks to optimize signal reconstruction. To benefit from the modification of the signal-to additive-signal ratio, it is proposed to decompose the action of the non-orthogonal transform of an arbitrary signal into a sum of transforms on the orthogonal components of the signal. The orthogonal components of the signal are given by projections of the signal on to eigenvectors of quadratic form of the transform. The amplification/attenuation factors of the orthogonal components are known and given by eigenvalues of the quadratic form. An example of benefits of the proposed signal reconstruction approach in a lossy image compression application is shown in the paper.