$K$-frames, as a new generalization of frames, have important applications, especially in sampling theory, to help us to reconstruct elements from a range of a bounded linear operator $K$ in a separable Hilbert space. In this paper, we focus on the reconstruction formulae to characterize all $K$-duals of a given $K$-frame. Also, we give several approaches for constructing $K$-frames.
"Some constructions of $K$-frames and their duals." Rocky Mountain J. Math. 47 (6) 1749 - 1764, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1749