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Table 1 Comparison of our method to state-of-the-art quantized matrix recovery method and 1-bit tensor recovery method

From: Tensor recovery from noisy and multi-level quantized measurements

Framework Recovery error (general) Recovery error (K=3) Recovery error (K=2)
General tensors (our work) \(O\left (\sqrt {\frac {r^{K-1}K\log K}{n^{K-1}}}\right)\) \(O\left (\frac {r}{n}\right)\) \(O\left (\sqrt {\frac {r}{n}}\right)\)
SVD-tensors (our work) \(O\left (\sqrt {\frac {rK\log K}{n^{K-1}}}\right)\) \(O\left (\frac {\sqrt {r}}{n}\right)\) \(O\left (\sqrt {\frac {r}{n}}\right)\)
Ghadermarzy et al. [43] \(O\left (\left (\frac {r^{3K-3}K}{n^{K-1}}\right)^{1/4}\right)\) \(O\left (\left (\frac {r^{3/2}}{n^{1/2}}\right)\right)\) \(O\left (\left (\frac {r^{3/4}}{n^{1/4}}\right)\right)\)
Gao et al. [4] (matrix rank) \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\) \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\) \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\)