Structure assisted compressed sensing reconstruction of undersampled AFM images

We just had a new paper published in Ultramicroscopy in the January, 2017 issue. This paper details a method for using weights in iterative thresholding algorithms to enhance the reconstruction of undersampled AFM images. For a broad range of test images our proposed weighted iterative threshold algorithms outperform both non-weighted iterative thresholding and l1 based methods.

Abstract

The use of compressed sensing in atomic force microscopy (AFM) can potentially speed-up image acquisition, lower probe-specimen interaction, or enable super resolution imaging. The idea in compressed sensing for AFM is to spatially undersample the specimen, i.e. only acquire a small fraction of the full image of it, and then use advanced computational techniques to reconstruct the remaining part of the image whenever this is possible. Our initial experiments have shown that it is possible to leverage inherent structure in acquired AFM images to improve image reconstruction. Thus, we have studied structure in the discrete cosine transform coefficients of typical AFM images. Based on this study, we propose a generic support structure model that may be used to improve the quality of the reconstructed AFM images. Furthermore, we propose a modification to the established iterative thresholding reconstruction algorithms that enables the use of our proposed structure model in the reconstruction process. Through a large set of reconstructions, the general reconstruction capability improvement achievable using our structured model is shown both quantitatively and qualitatively. Specifically, our experiments show that our proposed algorithm improves over established iterative thresholding algorithms by being able to reconstruct AFM images to a comparable quality using fewer measurements or equivalently obtaining a more detailed reconstruction for a fixed number of measurements.

Download

• The Elsevier version of the paper is available here, DOI: 10.1016/j.ultramic.2016.09.011.
• The accompanying Python source code and simulation results can be downloaded here, DOI: 10.5281/zenodo.60512
• A Jupyter Notebook that reproduces the figures in the paper is available here, DOI: 10.5278/vbn/projects/wISTwIHT
• The experiments in the paper also make use of the Magni package: https://github.com/SIP-AAU/Magni/