  This work considers the use of Total variation (TV) minimization in the
recovery of a given gradient sparse vector from Gaussian linear measurements.
It has been shown in recent studies that there exist a sharp phase transition
behavior in TV minimization in asymptotic regimes. The phase transition curve
specifies the boundary of success and failure of TV minimization for large
number of measurements. It is a challenging task to obtain a theoretical bound
that reflects this curve. In this work, we present a novel upper-bound that
suitably approximates this curve and is asymptotically sharp. Numerical results
show that our bound is closer to the empirical TV phase transition curve than
the previously known bound obtained by Kabanava.
