Higher-order tensor structured data arise in many imaging scenarios, including hyperspectral imaging and color video. The recovery of a tensor from an incomplete set of its entries, known as tensor completion, is crucial in applications like compression. Furthermore, in many cases observations are not only incomplete, but also highly quantized. Quantization is a critical step for high dimensional data transmission and storage in order to reduce storage requirements and power consumption, especially for energy-limited systems. In this paper, we propose a novel approach for the recovery of low-rank tensors from a small number of binary (1-bit) measurements. The proposed method, called 1-bit Tensor Completion, relies on the application of 1-bit matrix completion over different matricizations of the underlying tensor. Experimental results on hyperspectral images demonstrate that directly operating with the binary measurements, rather than treating them as real values, results in lower recovery error.
Anastasia Aidini, Grigorios Tsagkatakis, Panagiotis Tsakalides, "1-Bit Tensor Completion" in Proc. IS&T Int’l. Symp. on Electronic Imaging: Image Processing: Algorithms and Systems XVI, 2018, pp 261-1 - 261-6, https://doi.org/10.2352/ISSN.2470-1173.2018.13.IPAS-261