Matrix quadrature filterbanks for image processing

An innovative approach is presented to establish bidimensional (2D) linear-phase matrix quadrature filterbanks (MQF) directly from their matrix identities. It is well-known that two-channel quadrature filterbanks (QMF) have been successfully applied to signal and image processing. Bidimensional QMF filterbanks directly deduced from tensor-products of 1D QMF filterbanks is easy, straightforward, and convenient. They possess both the finite impulse response (FIR) and the perfect reconstruction (PR) properties, which are necessary for filterbanks' alias-free as well as magnitude and phase distortion-free characteristics. However, some additional desirable features are missing. These features include directional features, magnitude preservation, energy preservation, and energy compaction. Direct consideration from matrices yields more freedoms for the design of the new ingenuous MQF. A new MQF is designed and is applied to image compression. The rate-distortion performance shows that the proposed matrix wavelet has promising potential applications in image processing.