0

Because of my research work, I am reading this paper: PDE net. But I ran into a notation problem: In definition 2.1, I do not understand how $\textbf{q}[ \textbf{k} ]$ yields a real number. Therefore, I could not verify the authors' claims about the order of sum rules of the Haar wavelet frame filter bank and also the filter \begin{equation*} \textbf{q} = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \end{pmatrix} \end{equation*} I checked their citations and some other literatures, but most of them just said $\{\textbf{q}[\textbf{k}]\}$ is a sequence of real numbers, which does not help me to understand the order of sum rules at all. I am grateful if anyone could give me some hint about this notation.

BM Yoon
  • 83
  • 1
    Since $k \in \mathbb{Z}^2$, the obvious guess is to take $k$ as a pair of indices into the matrix, and 0 if it's outside the bounds of the matrix. Does not that work? – Ted Jan 14 '19 at 08:14
  • It works! I can't believe the authors put it in this way! I have been guessing it is about convolution at $\textbf{k}$. Thank you so much. – BM Yoon Jan 14 '19 at 08:29

0 Answers0