We present SparseDR, a novel differentiable rendering algorithm designed for sparse representations based on Signed Distance Fields (SDF). We leverage the Sparse Brick Set representation and propose an adaptation of redistancing for sparse SDFs. This enables SparseDR to surpass existing works in accuracy of surface reconstruction by increasing the effective resolution of the SDF representation. SparseDR is efficiently implemented in C++ and Vulkan, achieving several times shorter reconstruction time than other methods.