FastAFM Enabling Fast Image Acquisition for Atomic Force Microscopy using Compressed Sensing

This is the official project page of the project: Enabling Fast Image Acquisition for Atomic Force Microscopy using Compressed Sensing.

This is the place to look for project news, information about and links to software and publications resulting from the project.

The project is funded by The Danish Council for Independent Research | Technology and Production Sciences under grant number 1335-00278A / 12-134971.

News

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.

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Magni version 1.6.0 released

Our newest version of the Magni software package was just released on the 2nd of November. We have not usually mentioned new releases of the package on this website, but this particular release has some interesting features we hope some of you find particularly interesting.

The major new features in this release are approximate message passing (AMP) and generalised approximate message passing (GAMP) estimation algorithms for signal reconstruction. These new algorithms can be found in the magni.cs.reconstruction.amp and magni.cs.reconstruction.gamp modules, respectively. Note that the magni.cs sub-package contains algorithms applicable to compressed sensing (CS) and CS-like reconstruction problems in general - and not just atomic force microscopy (AFM).

If you are not familiar with the Magni package and are interested in compressed sensing and/or atomic force microscopy, we invite you to explore the functionality the package offers. It also contains various iterative thresholding reconstruction algorithms, dictionary and measurement matrices for 1D and 2D compressed sensing, various features for combining this with AFM imaging, and mechanisms for validating function input and storing meta-data to aid reproducibility.

The Magni package was designed and developed with a strong focus on well-tested, -validated and -documented code.

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  • The package can be found on GitHub where we continually release new versions: GitHub - release 1.6.0 here.
  • The package documentation can be read here: Magni documentation
  • The package can be installed from PyPI or from Anaconda.

Validating Function Arguments in Python Signal Processing Applications

We had a presentation at the 2016 Scientific Computing with Python (SciPy) conference on validation of function arguments in Python. This is an attempt at advancing correctness of results by providing an intuitive function argument validation scheme for Python signal processing applications. An accompanying paper has now been published in the conference proceedings. SciPy 2016 was held in Austin, Texas, USA, July 11 - 17, 2016.

Abstract

Python does not have a built-in mechanism to validate the value of function arguments. This can lead to nonsensical exceptions, unexpected behaviour, erroneous results and the like. In the present paper, we define the concept of so-called application-driven data types which place a layer of abstraction on top of Python data types. With this concept in mind, we discuss the current argument validation solutions of PyDBC, Traitlets and Numtraits, MyPy, PyValid, and PyContracts. We find that they share the issue of expressing the validation scheme in terms of Python objects rather than in terms of the data they hold. Consequently, we lay out a suggestion for a validation strategy including what qualifies as a validation scheme, how to create an interface which promotes both usability and readability, and which Python constructs to encourage using for validation encapsulation. A reference implementation of the suggested validation strategy is part of the open-source Python package, Magni which is thus presented along with a number of examples of the usages of this package.

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Storing Reproducible Results from Computational Experiments using Scientific Python Packages

We had a presentation at the 2016 Scientific Computing with Python (SciPy) conference on making computational experiments in Python reproducible. This is an attempt at advancing reproducibility of computational results by storing metadata describing the computational setup along with the results. An accompanying paper has now been published in the conference proceedings. SciPy 2016 was held in Austin, Texas, USA, July 11 - 17, 2016.

Abstract

Computational methods have become a prime branch of modern science. Unfortunately, retractions of papers in high-ranked journals due to erroneous computations as well as a general lack of reproducibility of results have led to a so-called credibility crisis. The answer from the scientific community has been an increased focus on implementing reproducible research in the computational sciences. Researchers and scientists have addressed this increasingly important problem by proposing best practices as well as making available tools for aiding in implementing them. We discuss and give an example of how to implement such best practices using scientific Python packages. Our focus is on how to store the relevant metadata along with the results of a computational experiment. We propose the use of JSON and the HDF5 database and detail a reference implementation in the Magni Python package. Further, we discuss the focuses and purposes of the broad range of available tools for making scientific computations reproducible. We pinpoint the particular use cases that we believe are better solved by storing metadata along with results the same HDF5 database. Storing metadata along with results is important in implementing reproducible research and it is readily achievable using scientific Python packages.

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Modelling Reconstruction Quality of Lissajous Undersampled Atomic Force Microscopy Images

Another paper of ours was presented at the 2016 IEEE International Symposium on Biomedical Imaging (ISBI) in Prague, Czech Republic, April 13-16, 2016.

Abstract

The reconstruction quality which can be obtained using compressive sensing depends on a number of elements. In the present paper, we establish performance indicators and use these to model the reconstruction quality of atomic force microscopy images undersampled with Lissajous sampling patterns. For this purpose, we consider previously proposed performance indicators. Furthermore, we propose new performance indicators based on the relative energy of the subsampled dictionary matrix atoms. Through extensive simulations, multiple affine models are evaluated in terms of modified coefficients of determination. The results show that the proposed performance indicators are highly correlated with the average reconstruction quality. In conclusion, the proposed performance indicators can be used to model reconstruction quality for the given application, and the proposed model outperforms the previously established model.

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Reconstruction Algorithms in Undersampled AFM Imaging

We just had a new paper published in IEEE Journal of Selected Topics in Signal Processing in the February, 2016 issue. This is an attempt to create an overview of some of the basic possibilities in sparse image reconstruction / inverse problems that can be used to reconstruct images from undersampled measurements in atomic force microscopy.

Abstract

This paper provides a study of spatial undersampling in atomic force microscopy (AFM) imaging followed by different image reconstruction techniques based on sparse approximation as well as interpolation. The main reasons for using undersampling is that it reduces the path length and thereby the scanning time as well as the amount of interaction between the AFM probe and the specimen. It can easily be applied on conventional AFM hardware. Due to undersampling, it is necessary to subsequently process the acquired image in order to reconstruct an approximation of the image. Based on real AFM cell images, our simulations reveal that using a simple raster scanning pattern in combination with conventional image interpolation performs very well. Moreover, this combination enables a reduction by a factor 10 of the scanning time while retaining an average reconstruction quality around 36 dB PSNR on the tested cell images.

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Predicting Reconstruction Quality within Compressive Sensing for Atomic Force Microscopy

Another paper of ours was presented at the 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP) in Orlando, Florida, USA, December 14-16, 2015.

Abstract

With compressive sensing, the obtainable reconstruction quality depends on the original signal, the reconstruction algorithm, the measurement matrix, and the dictionary matrix. The present paper is concerned with establishing performance indicators and using these to predict reconstruction quality in atomic force microscopy applications. For this purpose, we consider the well-known quantities of coherence and mutual coherence. Furthermore, we propose a new performance indicator derived from coherence in order to better model the average reconstruction quality. Through extensive simulations, affine models using the performance indicators are evaluated in terms of modified coefficients of determination. The results show that the proposed performance indicator yields a better model than both coherence and mutual coherence do. In conclusion, the proposed performance indicator can be used to predict reconstruction quality for the given application, and the affine prediction model can be improved by including coherence and mutual coherence.

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Magni: A Python Package for Compressive Sampling and Reconstruction of Atomic Force Microscopy Images

Our most recent paper was published in the Journal of Open Research Software on October 7, 2014. This is a “software meta-paper”, i.e. a paper describing our software package

Abstract

Magni is an open source Python package that embraces compressed sensing and Atomic Force Microscopy (AFM) imaging techniques. It provides AFM-specific functionality for undersampling and reconstructing images from AFM equipment and thereby accelerating the acquisition of AFM images. Magni also provides researchers in compressed sensing with a selection of algorithms for reconstructing undersampled general images, and offers a consistent and rigorous way to efficiently evaluate the researchers own developed reconstruction algorithms in terms of phase transitions. The package also serves as a convenient platform for researchers in compressed sensing aiming at obtaining a high degree of reproducibility of their research.

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Reconstruction of Undersampled Atomic Force Microscopy Images: Interpolation versus Basis Pursuit

The project’s first paper paper was presented at The 9th International Conference on Signal Image Technology and Internet Based Systems in Kyoto, Japan, December 2-5, 2013.

Abstract

Atomic force microscopy (AFM) is one of the most advanced tools for high-resolution imaging and manipulation of nanoscale matter. Unfortunately, standard AFM imaging requires a timescale on the order of seconds to minutes to acquire an image which makes it complicated to observe dynamic processes. Moreover, it is often required to take several images before a relevant observation region is identified. In this paper we show how to significantly reduce the image acquisition time by undersampling. The reconstruction of an undersampled AFM image can be viewed as an inpainting, interpolating problem, or a special case of compressed sensing. We argue that the preferred approach depends upon the type of image. Of the methods proposed for AFM, images containing high frequencies should be reconstructed using basis pursuit from data collected in a spiral pattern. Images without too much high frequency content should be reconstructed using interpolation.

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  • The original paper is available open access here (IEEExplore), DOI: 10.1109/SITIS.2013.32.
  • The paper is accessible through Aalborg University’s institutional repository, VBN, here: VBN