论文标题
快速扩展到磁盘上的谐波：通过快速径向卷积的可协调基础
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
论文作者
论文摘要
我们提出了一种快速且数值准确的方法，用于扩展数字化的$ l \ times l $图像，代表$ [-1,1]^2 $在磁盘$ \ {x \ in \ Mathbb {r}^2：| x | x | x | <1 \} $上支持的函数的功能（dirichleich laplacian eigenfuntions in \ dirichlet laplacian eigeNfunctions in \ mathbb {r}^2：| x | x | <1 \} $。我们称为快速磁盘谐波变换（FDHT）的方法，以$ O（l^2 \ log L）$操作运行。此基础也称为傅立叶贝斯尔基础，它具有多个计算优势：它是正交的，按频率订购，并且可以通过在基础上扩展的图像来通过将对角线变换应用于系数来旋转。此外，我们表明，具有径向函数的卷积也可以通过将对角变换应用于系数进行有效计算。
We present a fast and numerically accurate method for expanding digitized $L \times L$ images representing functions on $[-1,1]^2$ supported on the disk $\{x \in \mathbb{R}^2 : |x|<1\}$ in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we refer to as the Fast Disk Harmonics Transform (FDHT), runs in $O(L^2 \log L)$ operations. This basis is also known as the Fourier-Bessel basis, and it has several computational advantages: it is orthogonal, ordered by frequency, and steerable in the sense that images expanded in the basis can be rotated by applying a diagonal transform to the coefficients. Moreover, we show that convolution with radial functions can also be efficiently computed by applying a diagonal transform to the coefficients.
