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Blind Deconvolution of Telescope Imagery

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Left: video data of an orbiting satellite acquired by a ground based telescope. Right: restored video by blind deconvolution and contrast enhancement.

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Values of the maximum likelihood objective function for deconvolution with the different optimization methods. The red curve is the accelerated method that I developed, which improved the convergence by a factor of 5-10 over the standard algorithm (blue curve). Reference paper here.

Nanoscale 3D imaging from electron tomography

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Electron tomography reconstruction of a nano-particle based on the COM alignment method developed in [1,2]. On the left is a traditional alignment and reconstruction and on the right is the new work. The bright spots are platinum particles, which are not accurately captured with the tradition method.

[1] Toby Sanders, Micah Prange, Cem Akatay, and Peter Binev. Physically motivated global alignment method for electron tomography. Advanced Structural and Chemical Imaging, 1(1):1–11, 2015.

[2] Toby Sanders and Ilke Arslan. Improved three-dimensional (3D) resolution of electron tomograms using robust mathematical data-processing techniques. Microscopy and Microanalysis, 23(6):1121, 2017.

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Result from [3], where different regularization techniques were developed for electron tomography image reconstruction. Shown is a cross-sectional slice of a 3D nano-particle, where the HOTV regularization provides reduced noise and improved resolution.

[3] Toby Sanders, Anne Gelb, Rodrigo Platte, Ilke Arslan, and Kai Landskron. Recovering fine details from under-resolved electron tomography data using higher order total variation regularization. Ultramicroscopy, 174:97–105, 2017.

BM3D Image Restoration and De-blocking

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Left: severely corrupted and compressed overhead image. Right: automated image restoration using a multi-frame BM3D algorithm.

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Left: blurry and compressed natural image. Right: automated image restoration using a multi-frame BM3D deconvolution algorithm. Publication in progress.

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Left: noisy image of a cat in a hat. Right: denoised image using a single frame with fast BM3D image denoising.

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Execution times of the different Matlab-based BM3D algorithms as a function of the image size. Plotted is the speed up factor observed from our algorithm. Publication in progress.

[1] Toby Sanders and Sean Larkin. New Computational Techniques for a Faster Variation of BM3D Image Denoising. In preparation for IEEE Trans. on Im. Processing. 

Synthetic Aperture Radar Imaging

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(a) Diagram of SAR data acquisition. (b) Conventional SAR image reconstruction. (c) SAR image reconstruction from work in [1].

[1] Toby Sanders, Anne Gelb, and Rodrigo B Platte. Composite SAR imaging using sequential joint sparsity. Journal of Computational Physics, 338:357–370, 2017.

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Left: image reconstructed from conventional synthetic aperture radar (SAR). Middle: a denoising method developed by Lickenbrock that removes noise but leaves some of the natural texture that may be desirable in the SAR image. Right: an alternative denoising method developed by Lickenbrock.

Automated Image Classification Algorithms

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I have developed algorithms for automated detection and classification for several different applications. Above is an example of automated terrain classification that uses a random forest classifier.

Other Related Work

  • Image inpainting: 

    • Toby Sanders and Christian Dwyer. Subsampling and inpainting approaches for electron tomography. Ultramicroscopy, 182:292–302, 2017.

    • Toby Sanders and Chrisitna Dwyer. Inpainting versus denoising for dose reduction in scanning-beam microscopies. IEEE Transactions on Image Processing, 29:351–359, 2019.

  • Automated parameter selection: 

    • Toby Sanders, Rodrigo B Platte, and Robert D Skeel. Effective new methods for automated parameter selection in regularized inverse problems. Applied Numerical Mathematics, 152:29–48, 2020.

    • Toby Sanders. Parameter selection for HOTV regularization. Applied Numerical Mathematics, 125:1–9, 2018.

  • Discrete Tomography​: T. Sanders. Discrete iterative partial segmentation technique (DIPS) for tomographic reconstruction. IEEE Trans. Comput. Imag., 2(1):71–82, March 2016.

  • New regularization techniques: Toby Sanders and Rodrigo B Platte. Multiscale higher-order TV operators for L1 regularization. Advanced Structural and Chemical Imaging, 4(1):12, 2018.

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