Deep neural networks for understanding noisy data applied to physical property extraction in scanning probe microscopy

The rapid development of spectral-imaging methods in scanning probe, electron, and optical microscopy in the last decade have given rise for large multidimensional datasets. In many cases, the reduction of hyperspectral data to the lower-dimension materials-specific parameters is based on functional fitting, where an approximate form of the fitting function is known, but the parameters of the function need to be determined. However, functional fits of noisy data realized via iterative methods, such as least-square gradient descent, often yield spurious results and are very sensitive to initial guesses. Here, we demonstrate an approach for the reduction of the hyperspectral data using a deep neural network approach. A combined deep neural network/least-square approach is shown to improve the effective signal-to-noise ratio of band-excitation piezoresponse force microscopy by more than an order of magnitude, allowing characterization when very small driving signals are used or when a material’s response is weak