A Semi Nonnegative Matrix Factorization Technique for Pattern Generalization in Single-Pixel Imaging

Abstract

A single-pixel camera is a computational imaging device that only requires a single point detector to capture the image of a scene. This device measures the inner product of the scene and the spatial light modulator patterns. The image of the scene can be recovered through postprocessing the measurements obtained for a set of different patterns. Independent of the strategy used for image recovery, real acquisitions require the spatial light modulator patterns to be positive. In addition, the dark current measured in the absence of modulation must be rejected. To date, both experimental issues have been addressed empirically. In this paper, we solve these from a general perspective. Indeed, we propose to seek positive patterns that are linear combinations of the desired patterns (with negative values), and the linear transformation matrices are chosen to reject the dark current. We refer to the problem of finding the positive patterns and the linear combinations as “pattern generalization.” To the best of our knowledge, this is the first time that this problem has been introduced. In addition, we show that pattern generalization can be solved using a semi nonnegative matrix factorization algorithm. The data obtained from simulations demonstrate that our approach performs similarly to or better than conventional methods, while using fewer measurements.