Compressive Higher-order Sparse and Low-Rank Acquisition with a Hyperspectral Light Stage

Abstract

Compressive sparse and low-rank recovery (CSLR) is a novel method for compressed sensing deriving a low-rank and a sparse data terms from randomized projection measurements. While previous approaches either applied compressive measurements to phenomena assumed to be sparse or explicitly assume and measure low-rank approximations, CSLR is inherently robust if any such assumption might be violated. In this paper, we will derive CSLR using Fixed-Point Continuation algorithms, and extend this approach in order to exploit the correlation in high-order dimensions to further reduce the number of captured samples. Though generally applicable, we demonstrate the effectiveness of our approach on data sets captured with a novel hyperspectral light stage that can emit a distinct spectrum from each of the 196 light source directions enabling bispectral measurements of reflectance from arbitrary viewpoints. Bispectral reflectance fields and BTFs are faithfully reconstructed from a small number of compressed measurements.