Linear quantization by effective-resistance sampling

In this paper we consider the problem of allocation of measurement bits in order to reduce the statistical signal recovery error resulting from quantization error. We propose a continuous optimization problem that serves as a relaxation of the original combinatorial problem, which is amenable to classical continuous optimization solvers such as the gradient descent. We also design a "rounding" algorithm based on the idea of effective resistance sampling to turn the continuous fractional solution into a feasible bit allocation strategy with integer number of bits allocated to each design point.