Computation and Optimization of Frame Bounds for the Laplacian Pyramid
【摘要】：The Laplacian pyramid (LP) plays an important role in multiresolution processing. It can be viewed as a special oversampled filter bank (OFB) frame that provides a redundant signal representation. This paper studies the computation and optimization of frame bounds for the LP frame. For any given N-level LP, an algorithm is developed to compute its polyphase matrix, based on which the linear matrix inequality (LMI) conditions are provided to compute the frame bounds. We show that the frame bound ratio can be decreased by adjusting the gain of each sub-channel without changing frequency selective property. The minimal ratio as well as the corresponding optimal gain factors has been obtained by solving some LMIs, which can be easily solved by existing handy software. Various numerical examples are given to show the effectiveness of the proposed methods.