Recently we have proposed a new image device called the gigavision camera. The main feature of this camera is that the pixels have a binary response. The response function of a gigavision sensor is non-linear and similar to a logarithmic function, which makes the camera suitable for high dynamic range imaging. Since the sensor can detect a single photon, the camera is very sensitive and can be used for night vision and astronomical imaging. One important aspect of the gigavision camera is how to estimate the light intensity through binary observations. We model the light intensity field as 2D piecewise constant and use Maximum Penalized Likelihood Estimation (MPLE) to recover it. Dynamic programming is used to solve the optimization problem. Due to the complex computation of dynamic programming, greedy algorithm and pruning quadtrees are proposed. They show acceptable reconstruction performance with low computational complexity. Experimental results with synthesized images and real images taken by a single-photon avalanche diode (SPAD) camera are given.