Computational Imaging Models and Theory for Magnetic Particle Imaging (MPI)
MPI image reconstruction of a spiral test phantom.
[1] Sanders, Toby, et al. "A Physics-Based Computational Forward Model for Efficient Image Reconstruction in Magnetic Particle Imaging." IEEE Transactions on Medical Imaging (2025).
MPI image reconstruction of an in-vivo mouse to detect and image lymph nodes. The mouse outline is added for anatomical context.
[1] Sanders, Toby, et al. "A Physics-Based Computational Forward Model for Efficient Image Reconstruction in Magnetic Particle Imaging." IEEE Transactions on Medical Imaging (2025).
System matrix analysis using the operator sequence developed in this work. The top row visualizes the wave functions arising from our model at each of the harmonics, which shows how the new computational model matched previous simulation theory that had existed for over a decade without an existing model. In the bottom left is the Lissajous pattern used in this simulation, for which the new model was the first calibration free method that could handle such data. The remainder of the bottom row shows a few selected rows of the time domain operator A, i.e. the system’s response at particular time points.
[1] Sanders, Toby, et al. "A Physics-Based Computational Forward Model for Efficient Image Reconstruction in Magnetic Particle Imaging." IEEE Transactions on Medical Imaging (2025).
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.
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.