Wavelet Kalman based reconstruction

The analysis and synthesis operations of commonly used families of the discrete wavelet transform (DWT) are modeled within the framework of an ordinary Kalman filter (KF). In particular, the synthesis operation is regarded as the state evolution from a coarse subspace to a finer one. The analysis operation is considered as a partially observable process. It is shown that such descriptions provide for a natural and compact representation of the underlying signals. Extensions to image reconstruction and compression applications are demonstrated.