Frame Bound Computation of Two-dimensional Filter Bank Frames

The upper (lower) bound of a frame is an important index in the analysis and design of filter bank frames. There is lack of effectively numerical methods to compute the frame bounds for two-dimensional (2-D) filter banks (FBs). This paper investigates the computation problem of frame bounds and provides a frequency-independent solution. Firstly, the state space realization of 2-D FIR discrete FBs is given in the form of Roesser model. Then an LMI based optimization method is presented by using the generalized Kalman-Yakubovich-Popov (KYP) lemma. Finally, various examples are given on wavelet and Laplacian pyramid frames to demonstrate the effectiveness of the proposed method for 2-D frames.