Fig. 4: Benchmarking SBD-STM performance.
From: Dictionary learning in Fourier-transform scanning tunneling spectroscopy
a SBD-STM performance phase diagram from noise-free simulated results on images of area n = 256 × 256, plotting the error metric \(\epsilon ({\hat{{\mathcal{A}}}}_{\theta ,\eta },{{\mathcal{A}}}_{0})\) as a function of normalized kernel size and concentration θ (the number of defects scaled by the number of pixels). Each point on the diagram is determined from the mean of 20 independent simulated measurements. SBD-STM performs well in the blue regions, but begins to fail in the red regions, at very high kernel size or concentration. Green stars labeled A, B, C, D, and E indicate representative images from refs. 5,7,9,18,48, respectively. b Performance of SBD-STM in the presence of additive noise in the measurement at a fixed value of the normalized kernel size m∕n = 0.14. Error bars represent the standard deviation of the error metric from the 20 simulated measurements at each Kernel concentration. The inset shows the truth kernel used in the simulations. c–f Examples of simulated measurements from b and their corresponding SBD-STM recovered kernels. g–j A comparison of the Re-FTs of the measurement and the SBD-STM recovered kernel, indicating that SBD-STM consistently outperforms FT-STM across all parameter ranges. All Re-FT spectra are shown with − 3π/5a ≤ qx, qy ≤ 3π/5a, and color bars for c–j are in arbitrary units.
