  This paper proposes a combination of rotational compressive sensing with the
l1-l2 minimization to estimate coefficients of generalized polynomial chaos
(gPC) used in uncertainty quantification. In particular, we aim to identify a
rotation matrix such that the gPC of a set of random variables after the
rotation has a sparser representation. However, this rotational approach alters
the underlying linear system to be solved, which makes finding the sparse
coefficients much more difficult than the case without rotation. We further
adopt the l1-l2 minimization that is more suited for such ill-posed problems in
compressive sensing (CS) than the classic l1 approach. We conduct extensive
experiments on standard gPC problem settings, showing superior performance of
the proposed combination of rotation and l1-l2 minimization over the ones
without rotation and with rotation but using the l1 minimization.
