The most demanding tests involved micro-patterned structures imaged in non-contact topographic mode at 7.0 hertz, with slow scans at 0.5 hertz serving as references. Under these conditions, the microscope’s feedback loop cannot always follow abrupt changes in surface height. At an ascending edge, the probe can reach the surface before the controller responds, producing a collision overshoot. At a descending edge, the probe can lose contact and “parachute” above the surface, creating an undershoot. These directional artifacts become more pronounced as scan speed rises, degrading sharp step edges and limiting the rate at which nanoscale and microscale images can be collected.

Researchers addressed the problem with a denoising convolutional neural network, or DnCNN, that accepted four co-acquired inputs: trace topography, the difference between trace and retrace topography, and the error signals generated during the forward and backward scans. The trace–retrace difference acts as a spatial indicator of directional artifacts, approaching zero in relatively flat regions but changing at edges where the two scan directions behave differently. The error channels report residual probe deflection that the feedback controller failed to correct and can contain high-frequency structural information absent from the primary topography image. All four signals were produced during the normal scan using existing instrument outputs, without hardware modification or a separate reference acquisition at inference.

For topographic restoration, the network was configured to output a single-channel residual that was added to the trace-topography input. The four signals were concatenated along the channel dimension and fused through the first 3-by-3 convolutional layer, with no manual channel weighting or separate fusion module. Adding channels therefore changed only the first layer. The parameter increase attributable to the extra inputs was at most 1.5% for the smallest DnCNN and less than 0.5% for the other tested sizes. This simple arrangement allowed the model to use directional asymmetry and feedback residuals without introducing a large new processing architecture.

Channel ablations showed that the improvement was not merely a numerical effect from giving a network more inputs. With the smallest 57,000-parameter four-channel DnCNN, mean peak signal-to-noise ratio for the topographic restoration task reached 25.57 decibels, compared with 24.11 decibels for a 2.686-million-parameter single-channel Restormer. Removing the trace–retrace difference, trace error or retrace error individually reduced the mean result to 24.80, 24.75 and 24.53 decibels, respectively. Control inputs that repeated the primary image, substituted mismatched auxiliary data or added Gaussian noise matched to the auxiliary channel means and standard deviations produced 21.36, 19.90 and 20.12 decibels. These controls supported the contribution of spatially corresponding measurement information beyond increased input dimensionality.

A direct comparison with larger single-channel models produced a similar result. A 210,000-parameter four-channel DnCNN generated higher-quality restorations than single-channel U-Net and Restormer models containing 483,000 and 499,000 parameters, respectively. Line profiles through the test structures showed that the four-channel result most closely followed the slow-scan reference at sharp transitions, where both single-channel models smoothed over fine features. Across all tested parameter counts, the four-channel DnCNN delivered higher reported reconstruction quality than the single-channel architectures. Because both the information available to the model and the network design changed, the authors cautioned that this was not an architecture-only comparison.

The benefit grew as image degradation increased. The multi-channel gain in peak signal-to-noise ratio rose from 0.14 decibels at a scan speed of 1.0 hertz to 5.71 decibels at 7.0 hertz. The four-channel topographic models also reached their final structural similarity plateau within about 20 training epochs, compared with about 40 for single-channel models. Boundary-based measurements showed closer agreement with reference images: under a two-pixel matching tolerance, the F1 score for topographic step boundaries increased from 0.444 to 1.000, while the false-boundary fraction fell from 0.527 to zero. The four-channel approach also outperformed conventional trace–retrace averaging and Gaussian, median, Wiener and non-local-means filters, which produced peak signal-to-noise ratios between 17.48 and 18.77 decibels under the reported test conditions.

Speed was another practical advantage. The 57,000-parameter four-channel DnCNN required 1.13 milliseconds per 64-by-64-pixel patch, whereas the largest single-channel Restormer required 27.68 milliseconds. The accompanying comparison reported a 1.10-decibel quality advantage, approximately 47-fold fewer parameters and a 24-fold inference-speedup. A separate electrostatic force microscopy analysis found that a four-channel model using 6.37 million parameters achieved 25.76 decibels and a structural similarity index of 0.9125, comparable to 25.70 decibels and 0.9119 from a 12.74-million-parameter single-channel model. At a fixed 3.62-million-parameter capacity, a four-channel network trained on 25% of the available patches achieved 20.34 decibels and 0.6743, versus 20.13 decibels and 0.6486 for a single-channel network trained on 50%. Linear interpolation indicated that the multi-channel model needed about 2.1 times fewer training patches to match the same peak signal-to-noise ratio.

The approach was not limited to scan-direction artifacts. In electrostatic force microscopy, nanocapacitors measured at 3.0 hertz developed noise that obscured individual structures in the amplitude image, while the error channel retained recognizable features. A nonlinear activation-free-network U-Net using trace amplitude, retrace amplitude and two error channels recovered the nanocapacitor pattern more clearly than single- and two-channel models. In piezoresponse force microscopy, phase and amplitude signals are coupled through the material’s piezoelectric response, so amplitude data can help restore domain structure. For a polycrystalline lead zirconate titanate thin film, the four-channel reconstruction improved phase-image peak signal-to-noise ratio by 0.35–0.80 decibels over the single-channel result, with corresponding improvements in structural similarity and Pearson correlation. Boundary agreement also improved: the F1 score rose from 0.917 to 0.961 for PFM domain walls and from 0.968 to 0.982 for electrostatic-force feature boundaries.

Across the electrostatic-force and piezoresponse experiments, the authors estimated that models using auxiliary signals could reach a given image quality with 35% less reference-data acquisition time for electrostatic-force scan-speed noise, 25% less for piezoresponse scan-speed noise and 38% less for piezoresponse time-constant noise. These are modeled training-data savings based on the supplied measurements, not a universal reduction in routine microscope operation. The experimental collection was compact: 11 topographic trace–retrace image pairs yielded 6,896 augmented patches, while five image pairs for each electrostatic-force and piezoresponse condition yielded 3,136 augmented patches per condition. Source images were spatially partitioned, and training, validation and test patches did not share pixel content, reducing the risk of information leakage between evaluations.

The results support physics-guided channel selection as an alternative to indiscriminate model scaling, but the study also defines clear limits. Multi-channel fusion can be misleading if an auxiliary signal is saturated, excessively noisy, misregistered or more severely degraded than the primary measurement. Performance may also fall on samples, instruments, probes or distortion mechanisms outside the training distribution, including severe drift, abrupt tip changes and signal clipping. The framework also addresses restoration of dynamic acquisition artifacts, rather than general drift correction, tip-shape deconvolution or full inverse imaging. The authors therefore call for assessment of channel quality and independent validation before quantitative use under new measurement conditions, followed by retraining or fine-tuning when needed. Within those boundaries, the experiments show that signals already produced by atomic force microscopes can supply restoration networks with information unavailable from a single image channel, offering a more efficient route to faster and more accurate scientific imaging.

Subject of Research: Physics-guided multi-channel neural networks for restoring atomic force microscopy images

Article Title: Physics‐Guided Multi‐Channel Restoration for Efficient and Accurate Atomic Force Microscopy Imaging

Article References: Sung, J., Kim, H., Heo, S., Moon, J. T., Ko, J., Sriboriboon, P., Lee, D.-G., Jo, S., Han, H., Ryu, J., Lee, W., Heo, J., Song, H.-C., & Kim, Y. (2026). Physics‐Guided Multi‐Channel Restoration for Efficient and Accurate Atomic Force Microscopy Imaging. Advanced Science, Article e78289. https://doi.org/10.1002/advs.78289

Image Credits: AI Generated

DOI: 10.1002/advs.78289

Keywords: atomic force microscopy, image restoration, multi-channel learning, physics-guided AI, neural networks, scan artifacts, piezoresponse force microscopy, electrostatic force microscopy, deep learning, scientific imaging, Physics, Guided