  We propose a new approach to the problem of recovering signal from frame
coefficients with erasures. Such problems arise naturally from applications
where some of the coefficients could be corrupted or erased during the data
transmission. Provided that the erasure set satisfies the minimal redundancy
condition, we construct a suitable synthesizing dual frame which enables us to
perfectly reconstruct the original signal without recovering the lost
coefficients. Such dual frames which compensate for erasures are described from
various viewpoints.
  In the second part of the paper frames robust with respect to finitely many
erasures are investigated. We characterize all full spark frames for
finite-dimensional Hilbert spaces. In particular, we show that each full spark
frames is generated by a matrix whose all square submatrices are nonsingular.
In addition, we provide a method for constructing totally positive matrices.
Finally, we give a method, applicable to a large class of frames, for
transforming general frames into Parseval ones.
