محسن شاهرضایی - دانشکده علوم دفاعی، دانشگاه جامع امام حسین (ع)، تهران، ایران
علیرضا شجاعی فرد - گروه ریاضی و آمار، دانشکده و پژوهشکده علوم پایه، دانشگاه جامع امام حسین (ع)، تهران، ایران
حمیدرضا یزدانی - گروه ریاضی و آمار، دانشکده و پژوهشکده علوم پایه، دانشگاه جامع امام حسین (ع)، تهران، ایران

Higher-order tensor structured data appear in many imaging scenarios, including hyperspectral imaging and colorful video. The recovery of a tensor from an incomplete set of its entries, known as tensor completion (TC), is significant in applications like compression. Moreover, in many illustrations, 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 (۱-bit) measurements. The proposed method called ۱- bit Tensor Completion relies on the application of ۱-bit matrix completion over different matricizations of the underlying tensor. Experimental results on hyperspectral images confirm that directly operating with the binary measurements, rather than treating them as real values, results in lower recovery error. Here a given third-order tensor with binary arrays is recovered. In practice, we open the tensor as a ۳-matrix and apply the quantified tensor completion algorithm to all models of the matrix tensor. The data space here is distorted satellite spectral images for the purpose of image recovery.

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