Sparse coding and dictionary learning for electron hologram denoising

We demonstrate the effect of image denoising with sparse coding and dictionary learning algorithms for low-dose electron holography. Electron interference patterns (holograms) of a GaAs semiconductor specimen having a p-n junction were recorded with different exposure times (1, 4 and 40 s) and computer algorithms were applied to the holograms. The algorithms reduced the noise in the low-dose holograms successfully, with high data fidelity. In addition, the denoised holograms resulted in the phase images of a higher signal-to-noise ratio, fitting well to those obtained from original holograms recorded with sufficiently-long exposure times. The standard deviation in the reconstructed phase images was reduced by one digit using the denoising process. These results indicate that the sparse coding with dictionary learning algorithms are effective for electron holography and can potentially improve the temporal resolution by a factor of 40 or more without deterioration in the spatial resolution, thus enabling the observation of materials sensitive to electron beam irradiation and high-speed dynamical in situ electron holography.