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) | \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\) | \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\) | \(O\left (\sqrt {\frac {\bar {r}}{n}}\right)\) |