Bandwidth of trees of diameter at most 4

For a graph G, let γ:V(G)→1,⋯,|V(G)| be a one-to-one function. The bandwidth of γ is the maximum of |γ(u)-γ(v)| over uv∈E(G). The bandwidth of G, denoted b(G), is the minimum bandwidth over all embeddings γ, b(G)=min γmax|γ(u)-γ(v) |:uv∈E(G). In this paper, we show that the bandwidth computation problem for trees of diameter at most 4 can be solved in polynomial time. This naturally complements the result computing the bandwidth for 2-caterpillars. © 2012 Elsevier B.V. All rights reserved

Processing and inpainting of sparse data as applied to atomic force microscopy imaging

When data collection is expensive, gathering fewer and strategically located points may reduce costs while maintaining important information. Inpainting then allows for the intelligent reconstruction of missing data from the sparse observations. In this thesis work, we propose the least squares differences algorithm, a new scheme for de-trending data with repeated observations based on classical least squares fitting along with au empirical guideline for constructing good sampling strategies. Furthermore, we develop and present a novel inpainting algorithm – penalized dictionary inpainting – that utilizes a variable penalty term and exhibits nonlocal sensitivity. Armed with these two innovations, we illustrate how current atomic force microscopy (AFM) imaging can be made more efficient. In particular, we apply least squares differences to the analysis of non-raster scanning methodologies, along with the inpainting of sparse or subsampled data

Improved accuracy and speed in scanning probe microscopy by image reconstruction from non-gridded position sensor data.

Scanning probe microscopy (SPM) has facilitated many scientific discoveries utilizing its strengths of spatial resolution, non-destructive characterization and realistic in situ environments. However, accurate spatial data are required for quantitative applications but this is challenging for SPM especially when imaging at higher frame rates. We present a new operation mode for scanning probe microscopy that uses advanced image processing techniques to render accurate images based on position sensor data. This technique, which we call sensor inpainting, frees the scanner to no longer be at a specific location at a given time. This drastically reduces the engineering effort of position control and enables the use of scan waveforms that are better suited for the high inertia nanopositioners of SPM. While in raster scanning, typically only trace or retrace images are used for display, in Archimedean spiral scans 100% of the data can be displayed and at least a two-fold increase in temporal or spatial resolution is achieved. In the new mode, the grid size of the final generated image is an independent variable. Inpainting to a few times more pixels than the samples creates images that more accurately represent the ground truth

Improved accuracy and speed in scanning probe microscopy by image reconstruction from non-gridded position sensor data.

Scanning probe microscopy (SPM) has facilitated many scientific discoveries utilizing its strengths of spatial resolution, non-destructive characterization and realistic in situ environments. However, accurate spatial data are required for quantitative applications but this is challenging for SPM especially when imaging at higher frame rates. We present a new operation mode for scanning probe microscopy that uses advanced image processing techniques to render accurate images based on position sensor data. This technique, which we call sensor inpainting, frees the scanner to no longer be at a specific location at a given time. This drastically reduces the engineering effort of position control and enables the use of scan waveforms that are better suited for the high inertia nanopositioners of SPM. While in raster scanning, typically only trace or retrace images are used for display, in Archimedean spiral scans 100% of the data can be displayed and at least a two-fold increase in temporal or spatial resolution is achieved. In the new mode, the grid size of the final generated image is an independent variable. Inpainting to a few times more pixels than the samples creates images that more accurately represent the ground truth

Height drift correction in non-raster atomic force microscopy.

We propose a novel method to detect and correct drift in non-raster scanning probe microscopy. In conventional raster scanning drift is usually corrected by subtracting a fitted polynomial from each scan line, but sample tilt or large topographic features can result in severe artifacts. Our method uses self-intersecting scan paths to distinguish drift from topographic features. Observing the height differences when passing the same position at different times enables the reconstruction of a continuous function of drift. We show that a small number of self-intersections is adequate for automatic and reliable drift correction. Additionally, we introduce a fitness function which provides a quantitative measure of drift correctability for any arbitrary scan shape

Height drift correction in non-raster atomic force microscopy.

We propose a novel method to detect and correct drift in non-raster scanning probe microscopy. In conventional raster scanning drift is usually corrected by subtracting a fitted polynomial from each scan line, but sample tilt or large topographic features can result in severe artifacts. Our method uses self-intersecting scan paths to distinguish drift from topographic features. Observing the height differences when passing the same position at different times enables the reconstruction of a continuous function of drift. We show that a small number of self-intersections is adequate for automatic and reliable drift correction. Additionally, we introduce a fitness function which provides a quantitative measure of drift correctability for any arbitrary scan shape