In this paper, we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set E. Starting from a frame \((x_n)_{n=1}^\infty \) and its arbitrary dual frame, we give sufficient conditions for constructing a dual frame of \((x_n)_{n\in E^c}\) so that the perfect reconstruction can be obtained from the preserved frame coefficients. The work is motivated by methods using the canonical dual frame of \((x_n)_{n=1}^\infty \), which however do not extend automatically to the case when the canonical dual is replaced with another dual frame. The differences between the cases when the starting dual frame is the canonical dual and when it is not the canonical dual are investigated. We also give several ways of computing a dual of the reduced frame, among which we are the most interested in the iterative procedure for computing this dual frame.

在本文中，我们研究了从带有擦除的帧系数中恢复信号的问题。假设擦除的系数由有限集E索引。从一个框架\((x_n)_{n=1}^\infty \)及其任意对偶框架开始，我们给出构造\((x_n)_{n\in E^c}的对偶框架的充分条件\)以便从保留的帧系数中获得完美的重建。这项工作的动机是使用规范对偶框架\((x_n)_{n=1}^\infty \) 的方法，但是，当规范对偶框架被另一个对偶框架替换时，这些方法不会自动扩展到这种情况。研究了起始对偶帧是规范对偶帧和不是规范对偶帧时的情况之间的差异。我们还给出了计算简化帧的对偶的几种方法，其中我们最感兴趣的是计算此对偶帧的迭代过程。