We present a novel method for capturing real-world, spatially-varying surface reflectance from a small number of object views (k). Our key observation is that a specific target’s reflectance can be represented by a small number of custom basis materials (N) convexly blended by an even smaller number of non-zero weights at each point (n). Based on this sparse basis/sparser blend model, we develop an SVBRDF reconstruction algorithm that jointly solves for n, N, the basis BRDFs, and their spatial blend weights with an alternating iterative optimization, each step of which solves a linearly-constrained quadratic programming problem. We develop a numerical tool that lets us estimate the number of views required and analyze the effect of lighting and geometry on reconstruction quality. We validate our method with images rendered from synthetic BRDFs, and demonstrate convincing results on real objects of pre-scanned shape and lit by uncontrolled natural illumination, from very few or even a single input image.