  Random sampling in compressive sensing (CS) enables the compression of large
amounts of input signals in an efficient manner, which is useful for many
applications. CS reconstructs the compressed signals exactly with overwhelming
probability when incoming data can be sparsely represented with a few
components. However, the theory of CS framework including random sampling has
been focused on exact recovery of signal; impreciseness in signal recovery has
been neglected. This can be problematic when there is uncertainty in the number
of sparse components such as signal sparsity in dynamic systems that can change
over time. We present a new theoretical framework that handles uncertainty in
signal recovery from the perspective of recovery success and quality. We show
that the signal recovery success in our model is more accurate than the success
probability analysis in the CS framework. Our model is then extended to the
case where the success or failure of signal recovery can be relaxed. We
represent the number of components included in signal recovery with a
right-tailed distribution and focus on recovery quality. Experimental results
confirm the accuracy of our model in dynamic systems.
