Reconstruction of elevation maps from a collection of SAR images obtained in interferometric configuration is a challenging task. Reconstruction methods must overcome two adverse effects: the strong interferometric noise that contaminates the data, and the 2π phase ambiguities. Interferometric noise requires some form of smoothing among pixels of identical height. Phase ambiguities can be solved, up to a point, by combining linkage to the neighbors and a global optimization strategy to prevent from being trapped in local minima. This paper introduces a reconstruction method, PARISAR, that achieves both a resolution-preserving denoising and a robust phase unwrapping by combining non-local denoising methods based on patch similarities and total-variation regularization. The optimization algorithm, based on graph-cuts, identifies the global optimum. We compare PARISAR with several other reconstruction methods both on numerical simulations and satellite images and show a qualitative and quantitative improvement over state-of-the-art reconstruction methods for multi-baseline SAR interferometry.