  Tensors in the form of multilinear arrays are ubiquitous in data science
applications. Captured real-world data, including video, hyperspectral images,
and discretized physical systems, naturally occur as tensors and often come
with attendant noise. Under the additive noise model and with the assumption
that the underlying clean tensor has low rank, many denoising methods have been
created that utilize tensor decomposition to effect denoising through low rank
tensor approximation. However, all such decomposition methods require
estimating the tensor rank, or related measures such as the tensor spectral and
nuclear norms, all of which are NP-hard problems.
  In this work we leverage our previously developed framework of
$\textit{tensor amplification}$, which provides good approximations of the
spectral and nuclear tensor norms, to denoising synthetic tensors of various
sizes, ranks, and noise levels, along with real-world tensors derived from
physiological signals. We also introduce two new notions of tensor rank --
$\textit{stable slice rank}$ and $\textit{stable }$$X$$\textit{-rank}$ -- and
new denoising methods based on their estimation. The experimental results show
that in the low rank context, tensor-based amplification provides comparable
denoising performance in high signal-to-noise ratio (SNR) settings and superior
performance in noisy (i.e., low SNR) settings, while the stable $X$-rank method
achieves superior denoising performance on the physiological signal data.
