  We propose a framework called ReFInE to directly obtain integral image
estimates from a very small number of spatially multiplexed measurements of the
scene without iterative reconstruction of any auxiliary image, and demonstrate
their practical utility in visual object tracking. Specifically, we design
measurement matrices which are tailored to facilitate extremely fast estimation
of the integral image, by using a single-shot linear operation on the measured
vector. Leveraging a prior model for the images, we formulate a nuclear norm
minimization problem with second order conic constraints to jointly obtain the
measurement matrix and the linear operator. Through qualitative and
quantitative experiments, we show that high quality integral image estimates
can be obtained using our framework at very low measurement rates. Further, on
a standard dataset of 50 videos, we present object tracking results which are
comparable to the state-of-the-art methods, even at an extremely low
measurement rate of 1%.
