Patch-based texture synthesis has proven to produce high quality textures faster than pixel-based approaches. Previous algorithms differ in how the regions of overlap between neighboring patches are treated. We present an approach that produces higher quality overlap regions than simple blending of patches or computing good boundaries, however, that is faster than re-synthesizing invalid pixels using a classical per-pixel synthesis algorithm: we use a k-nearest neighbor (knn) data structure, obtained from the input texture in a precomputation step. Results from our implementation show that the algorithm produces high-quality textures, where the time complexity of the synthesis stage is linear in the number of re-synthesized pixels and, therefore, scales well with the size of the input texture. Patch-based Texture Synthesis, Principal Component Analysis, k-coherence search.