Second-Generation Curvelets on the Sphere
Second-Generation Curvelets on the Sphere
复制标题
DOI：
10.1109/tsp.2016.2600506
复制
发表时间：
2015-11
影响因子：
5.4
通讯作者：
Jennifer Y. H. Chan;B. Leistedt;T. Kitching;J. McEwen
中科院分区：
文献类型：
--
作者：
Jennifer Y. H. Chan;B. Leistedt;T. Kitching;J. McEwen
曲波对于表示高度各向异性的信号内容是有效的，例如局部线性和曲线结构。然而，球体上的第一代曲波受到阻塞伪影的影响。我们提出了一种新的第二代曲波变换，尺度离散曲波直接构造在球体上。尺度离散化曲线波表现出抛物线尺度关系，在空间和谐波域都很好地本地化，支持标量和自旋信号的精确分析和合成，并且没有阻塞伪影。我们提出了快速算法来计算精确的曲波变换，降低了计算复杂度从O（L5）到O（L3 log2 L）的信号带限在L。这些算法的实现是公开的。最后，我们提出了一个说明性的应用程序，证明了curvelets的有效性，表示方向曲线的功能，在自然的球形图像。
Curvelets are efficient to represent highly anisotropic signal content, such as a local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new second-generation curvelet transform, where scale-discretized curvelets are constructed directly on the sphere. Scale-discretized curvelets exhibit a parabolic scaling relation, are well localized in both spatial and harmonic domains, support the exact analysis and synthesis of both scalar and spin signals, and are free of blocking artefacts. We present fast algorithms to compute the exact curvelet transform, reducing computational complexity from O(L5) to O(L3 log2 L) for signals band limited at L. The implementation of these algorithms is made publicly available. Finally, we present an illustrative application demonstrating the effectiveness of curvelets for representing directional curve-like features in natural spherical images.