Toby Sanders

Physically motivated global alignment method for electron tomography

Electron tomography is widely used for nanoscale determination of 3-D structures in many areas of science. Determining the 3-D structure of a sample from electron tomography involves three major steps: acquisition of sequence of 2-D projection images of the sample with the electron microscope, alignment of the images to a common coordinate system, and 3-D reconstruction and segmentation of the sample from the aligned image data. The resolution of the 3-D reconstruction is directly influenced by the accuracy of the alignment, and therefore, it is crucial to have a robust and dependable alignment method. In this paper, we develop a new alignment method which avoids the use of markers and instead traces the computed paths of many identifiable ‘local’ center-of-mass points as the sample is rotated. Compared with traditional correlation schemes, the alignment method presented here is resistant to cumulative error observed from correlation techniques, has very rigorous mathematical justification, and is very robust since many points and paths are used, all of which inevitably improves the quality of the reconstruction and confidence in the scientific results.

Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ1 regularization

Over the last decade or so, reconstruction methods using ℓ1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images - even those for which TV was designed for - particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. We develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

Composite SAR imaging using sequential joint sparsity

Abstract This paper investigates accurate and efficient l 1 regularization methods for generating synthetic aperture radar (SAR) images. Although l 1 regularization algorithms are already employed in SAR imaging, practical and efficient implementation in terms of real time imaging remain a challenge. Here we demonstrate that fast numerical operators can be used to robustly implement l 1 regularization methods that are as or more efficient than traditional approaches such as back projection, while providing superior image quality. In particular, we develop a sequential joint sparsity model for composite SAR imaging which naturally combines the joint sparsity methodology with composite SAR. Our technique, which can be implemented using standard, fractional, or higher order total variation regularization, is able to reduce the effects of speckle and other noisy artifacts with little additional computational cost. Finally we show that generalizing total variation regularization to non-integer and higher orders provides improved flexibility and robustness for SAR imaging.

Discrete Iterative Partial Segmentation Technique (DIPS) for Tomographic Reconstruction

Discrete tomography refers to tomographic reconstruction of images that are known to contain only a few intensity levels. We propose a new reconstruction technique for discrete tomography that uses a relaxed partial segmentation and a refinement update in each iteration. With our approach the dimension of the tomographic reconstruction problem is carefully and slowly reduced as the image structures become more evident, allowing us to capture object details more accurately. The method is complemented with an appropriate sparsity model to incorporate the prior knowledge of the nature of the data and further improve the reconstruction. As a proof of concept, we compare our method with the current standard and state-of-the art techniques and in simulation experiments show substantial improvement in the accuracy of the reconstruction in all of the simulation cases considered as well as moderate improvement on experimental data.

Subsampling and inpainting approaches for electron tomography

With the aim of addressing the issue of sample damage during electron tomography data acquisition, we propose a number of new reconstruction strategies based on subsampling (which uses only a subset of a full image) and inpainting (recovery of a full image from subsampled one). We point out that the total-variation (TV) inpainting model commonly used to inpaint subsampled images may be inappropriate for 2D projection images of typical TEM specimens. Thus, we propose higher-order TV (HOTV) inpainting, which accommodates the fact that projection images may be inherently smooth, as a more suitable image inpainting scheme. We also describe how the HOTV method can be extended to 3D, a scheme which makes use of both image data and sinogram data. Additionally, we propose gradient subsampling as a more efficient scheme than random subsampling. We make a rigorous comparison of our proposed new reconstruction schemes with existing ones. The new schemes are demonstrated to perform better than or as well as existing schemes, and we show that they outperform existing schemes at low subsampling rates.

Combination of correlated phase error correction and sparsity models for SAR

Direct image formation in synthetic aperture radar (SAR) involves processing of data modeled as Fourier coefficients along a polar grid. Often in such data acquisition processes, imperfections in the data cannot simply be modeled as additive or even multiplicative noise errors. In the case of SAR, errors in the data can exist due to imprecise estimation of the round trip wave propagation time, which manifests as phase errors in the Fourier domain. To correct for these errors, we propose a phase correction scheme that relies on both the on smoothness characteristics of the image and the phase corrections associated with neighboring pulses, which are possibly highly correlated due to the nature of the data off setting. Our model takes advantage of these correlations and smoothness characteristics simultaneously for a new autofocusing approach, and our algorithm for the proposed model alternates between approximate image feature and phase correction minimizers to the model.

Advanced 3-D Reconstruction Algorithms for Electron Tomography

htmlabstractElectron tomography in the physical sciences has become a powerful tool for nanomaterial analysis. Recently, electron tomography is finding applications in more beam sensitive materials such as catalysts. For beam sensitive materials, the goal is to acquire the smallest number of images as possible but still maintain an accurate and high resolution 3-D reconstruction. Standard methods of 3D reconstruction, such as weighted back projection (WBP) and simultaneous iterative reconstruction technique (SIRT), are not equipped to handle this lack of information, and create significant blurring. This gives rise to a search for new methods of reconstruction. Two of the recent successful algorithms are the discrete algebraic reconstruction technique (DART) and total variation (TV) minimization within compressed sensing (CS). The DART algorithm uses ART and pairs it with the prior knowledge that there are only a small number (two or three) of different materials in the sample, each corresponding to a different gray value in the reconstruction. An initial reconstruction is computed and rounded to the chosen fixed gray values based on some threshold, and iteratively refined using ART. The method of TV minimization stems from the mathematical theory of compressed sensing and only recently became available due to new algorithms for solving the TV minimization problem. The method considers the characterization of real images and encourages the reconstruction to take larger jumps in gray values to create clear boundaries, hence creating a similar effect to that of DART. The advantage of DART is that an accurate selection of the gray values and the rounding procedure for the reconstruction gives extremely valuable information otherwise not available in any other reconstruction technique. The TV minimization procedure has fewer parameter selections, giving a stable method for reconstruction. Moreover, the introduction of the TV norm has the potential for creating boundaries alternate to what a DART reconstruction would find. Both methods are extremely valuable. In this presentation we discuss the pros and cons of each method, and show examples to illustrate when to use one method over the other. One comparison is shown in Figures 1-2 to demonstrate the differences for a layered zeolite material. This research was funded in part by the DOE BES DE-SC0005822 and the LDRD and Chemical Imaging Initiative programs at PNNL. The Pacific Northwest National Laboratory is operated by Battelle under contract DE-AC05-76RL01830.

Multiscale higher-order TV operators for L1 regularization

In the realm of signal and image denoising and reconstruction,

Robust Physical Alignment Models for Electron Tomography

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