We present and study linear programming based detectors for two-dimensional intersymbol interference channels. Interesting instances of two-dimensional intersymbol interference channels are magnetic storage, optical storage and Wyner's cellular network model. We show that the optimal maximum a posteriori detection in such channels lends itself to a natural linear programming based sub-optimal detector. We call this the Pairwise linear program detector. Our experiments show that the Pairwise linear program detector performs poorly. We then propose two methods to strengthen our detector. These detectors are based on systematically enhancing the Pairwise linear program. The first one, the Block linear program detector adds higher order potential functions in an exhaustive manner, as constraints, to the Pairwise linear program detector. We show by experiments that the Block linear program detector has performance close to the optimal detector. We then develop another detector by adaptively adding frustrated cycles to the Pairwise linear program detector. Empirically, this detector also has performance close to the optimal one and turns out to be less complex then the Block linear program detector.