  Over the past years, there are increasing interests in recovering the signals
from undersampling data where such signals are sparse under some orthogonal
dictionary or tight framework, which is referred to be sparse synthetic model.
More recently, its counterpart, i.e., the sparse analysis model, has also
attracted researcher's attentions where many practical signals which are sparse
in the truly redundant dictionary are concerned. This short paper presents
important complement to the results in existing literatures for treating sparse
analysis model. Firstly, we give the natural generalization of well-known
restricted isometry property (RIP) to deal with sparse analysis model, where
the truly arbitrary incoherent dictionary is considered. Secondly, we studied
the theoretical guarantee for the accurate recovery of signal which is sparse
in general redundant dictionaries through solving l1-norm sparsity-promoted
optimization problem. This work shows not only that compressed sensing is
viable in the context of sparse analysis, but also that accurate recovery is
possible via solving l1-minimization problem.
