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Computation and optimization of frame bounds for the Laplacian pyramid

机译:拉普拉斯金字塔帧界限的计算与优化

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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-Ievel 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.
机译:拉普拉斯金字塔(LP)在多分辨率处理中起着重要作用。它可以被视为一个特殊的过映原滤波器组(OFB)帧,提供冗余信号表示。本文研究了LP帧的帧界的计算和优化。对于任何给定的N-IEVEL LP,开发了一种算法以计算其多相矩阵,基于该算法基于提供线性矩阵不等式(LMI)条件来计算帧界限。我们表明,通过调整每个子信道的增益,可以通过在不改变频率选择性的情况下调整每个子信道的增益来降低帧边界比。通过求解一些LMI来获得最小的比率以及相应的最佳增益因子,可以通过现有的方便软件容易地解决。给出了各种数值例子来显示所提出的方法的有效性。

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