Noise learning of instruments for high-contrast, high-resolution and fast hyperspectral microscopy and nanoscopy.

The low scattering efficiency of Raman scattering makes it challenging to simultaneously achieve good signal-to-noise ratio (SNR), high imaging speed, and adequate spatial and spectral resolutions. Here, we report a noise learning (NL) approach that estimates the intrinsic noise distribution of each instrument by statistically learning the noise in the pixel-spatial frequency domain. The estimated noise is then removed from the noisy spectra. This enhances the SNR by ca. 10 folds, and suppresses the mean-square error by almost 150 folds. NL allows us to improve the positioning accuracy and spatial resolution and largely eliminates the impact of thermal drift on tip-enhanced Raman spectroscopic nanoimaging. NL is also applicable to enhance SNR in fluorescence and photoluminescence imaging. Our method manages the ground truth spectra and the instrumental noise simultaneously within the training dataset, which bypasses the tedious labelling of huge dataset required in conventional deep learning, potentially shifting deep learning from sample-dependent to instrument-dependent.