Image Bit-Depth Enhancement via Maximum A Posteriori Estimation of AC Signal

When images at low bit-depth are rendered at high bit-depth displays, missing least significant bits needs to be estimated. We study the image bit-depth enhancement problem: estimating an original image from its quantized version from a minimum mean squared error (MMSE) perspective. We first argue that a graph-signal smoothness prior-one defined on a graph embedding the image structure-is an appropriate prior for the bit-depth enhancement problem. We next show that directly solving for the MMSE solution is, in general, too computationally expensive to be practical. We then propose an efficient approximation strategy. In particular, we first estimate the ac component of the desired signal in a maximum a posteriori formulation, efficiently computed via convex programming. We then compute the dc component with an MMSE criterion in a closed form given the computed ac component. Experiments show that our proposed two-step approach has improved performance over the conventional bit-depth enhancement schemes in both objective and subjective comparisons.