Blind Deconvolution of Telescope Imagery

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

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

75nm

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.

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

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

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

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

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

(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.

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

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.