In this paper we continue our work in [13] where the minimization problem $I(\mu ):={\inf }_{\nu \in \mathcal{T}}{W}_2^2(\mu ,\nu ),\mathcal{T}$ being the set of probabilistic tight frames in ${\mathbb{R}}^d$ and $W_2$ the quadratic Wasserstein metric for measures, was solved in the particular case when the mean vector of the probabilistic frame μ is zero. The present work solves this problem in the general case, and in addition, establishes the uniqueness of the optimum and gives its explicit expression. The resolution of this problem is obtained by solving first the minimization problem $I_p(\mu ):={\inf }_{\nu \in {\mathcal{T}}_p}{W}_2^2(\mu ,\nu )$, where ${\mathcal{T}}_p$ stands for the set of all Parseval probabilistic tight frames in ${\mathbb{R}}^d$.

在本文中，我们在[13]中继续我们的工作，其中最小化问题 $\mathrm{一世}（\mu ）：={\mathrm{信息}}_{\nu \in \mathcal{Ť}}{\mathrm{w\; ^}}_2^2（\mu ，\nu ），\mathcal{Ť}$ 是概率概率紧框架的集合 ${\mathbb{[R}}^d$ 和 ${\mathrm{w\; ^}}_2$在概率框架μ的均值向量为零的特定情况下，解决了测量的二次Wasserstein度量。目前的工作在一般情况下解决了这个问题，此外，建立了最优值的唯一性并给出了它的明确表示。通过首先解决最小化问题来获得此问题的解决方案${\mathrm{一世}}_p（\mu ）：={\mathrm{信息}}_{\nu \in {\mathcal{Ť}}_p}{\mathrm{w\; ^}}_2^2（\mu ，\nu ）$，在哪里 ${\mathcal{Ť}}_p$ 代表所有Parseval概率紧框架的集合 ${\mathbb{[R}}^d$。