Multiresolution analysis based on FWT (Fast Wavelet Transform) is now widely used in scientific visualization. Spherical biorthogonal wavelets for spherical triangular grids were introduced by P. Schroder and W. Sweldens (1995). In order to improve on the orthogonality of the wavelets, the concept of nearly orthogonality, and two new piecewise-constant (Haar) bases were introduced by G.M. Nielson (1997). We extend the results of Nielson. First we give two one-parameter families of triangular Haar wavelet bases that are nearly orthogonal in the sense of Nielson. Then we introduce a measure of orthogonality. This measure vanishes for orthogonal bases. Eventually, we show that we can find an optimal parameter of our wavelet families, for which the measure of orthogonality is minimized. Several numerical and visual examples for a spherical topographic data set illustrates our results.
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机译：基于FWT（快照小波变换）的多分辨率分析现在广泛用于科学可视化。 P. Schroder和W. Sweldens（1995）引入了球形三角网格的球形双正交小波。为了改善小波的正交性，G.M.1引入了几乎正交性的概念和两种新的分段常数（HAAR）基地。尼尔森（1997年）。我们延长了尼尔森的结果。首先，我们给出两个三角形哈尔小波底座的一个参数系列，这些基座几乎正交。然后我们介绍了正交性的衡量标准。这项措施消失了正交的基础。最终，我们表明我们可以找到我们的小波家庭的最佳参数，其偏离元素的测量是最小化的。用于球形地形数据集的几个数值和视觉示例说明了我们的结果。
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