Complex sentence: This problem setup also allows for the dimensionality of representation space being higher than the one of the input space which results in seemingly redundant atoms allowing for multiple reconstruction ways but also providing an improvement in sparsity and flexibility of the representation.
Split into simpler sentences: This problem setup also allows the dimensionality of representation space to be higher than the one of the input space. The above two properties lead to having seemingly redundant atoms that allow multiple reconstruction ways but also provide an improvement in sparsity and flexibility of the representation.