Framing pyramids
Framing pyramids
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DOI：
10.1109/tsp.2003.815389
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发表时间：
2003-09-01
影响因子：
5.4
通讯作者：
Vetterli, M
中科院分区：
文献类型：
--
作者：
Do, MN;Vetterli, M
1983年，Burt和Adelson引入了拉普拉斯金字塔(LP)作为图像的多分辨率表示。我们用框架理论来研究LP，这揭示了通常的重构是次优的。我们证明了具有正交滤波的LP是一个紧框架，因此，使用对偶框架算子的最优线性重构具有简单的对称结构，并且具有前向变换。在更一般的情况下，我们提出了一种有效的滤波器组(FB)，用于使用投影来重建LP，该方法在存在噪声的情况下比通常的方法有了明显的改善。将LP设置为过采样的FB，我们提供了所有合成FB的完全参数化，从而为LP提供了完美的重建。最后，我们考虑了LP格式被迭代的情况，并推导出了与LP格式相关的连续域框架。
In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filters is a tight frame, and thus, the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric, with the forward transform. In more general cases, we propose an efficient filterbank (FB) for the reconstruction of the LP using projection that leads to a proved improvement over the usual method in the presence of noise. Setting up the LP as an oversampled FB, we offer a complete parameterization of all synthesis FBs that provide perfect reconstruction for the LP. Finally, we consider the situation where the LP scheme is iterated and derive the continuous-domain frames associated with the LP.