We introduce the prime coset sum method for constructing tight wavelet frames, which allows one to construct nonseparable multivariate tight wavelet frames with prime dilation, using a univariate lowpass mask with this same prime dilation as input. This method relies on the idea of finding a sum of hermitian squares representation for a nonnegative trigonometric polynomial related to the sub-QMF condition for the lowpass mask. We prove the existence of these representations under some conditions on the input lowpass mask, utilizing the special structure of the recently introduced prime coset sum method, which is used to generate the lowpass masks in our construction. We also prove guarantees on the vanishing moments of the wavelets arising from this method, some of which hold more generally.

我们介绍了用于构造紧小波框架的素数集估计方法，该方法允许使用具有相同素数膨胀作为输入的单变量低通蒙版来构造具有素数膨胀的不可分离的多元紧小波框架。该方法依赖于为与低通掩模的子QMF条件相关的非负三角多项式找到埃尔米特平方表示之和的想法。我们利用最近引入的素数陪集求和方法的特殊结构，在输入低通掩码上的某些条件下证明了这些表示的存在，该方法用于在我们的构造中生成低通掩码。我们还证明了由这种方法引起的小波消失矩的保证，其中一些更普遍。