  Numerous applications in signal processing have benefited from the theory of
compressed sensing which shows that it is possible to reconstruct signals
sampled below the Nyquist rate when certain conditions are satisfied. One of
these conditions is that there exists a known transform that represents the
signal with a sufficiently small number of non-zero coefficients. However when
the signal to be reconstructed is composed of moving images or volumes, it is
challenging to form such regularization constraints with traditional transforms
such as wavelets. In this paper, we present a motion compensating prior for
such signals that is derived directly from the optical flow constraint and can
utilize the motion information during compressed sensing reconstruction.
Proposed regularization method can be used in a wide variety of applications
involving compressed sensing and images or volumes of moving and deforming
objects. It is also shown that it is possible to estimate the signal and the
motion jointly or separately. Practical examples from magnetic resonance
imaging has been presented to demonstrate the benefit of the proposed method.
