There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://users.fmrib.ox.ac.uk/~jesper/papers/readgroup_071009/Ashburner07.pdf

A fast diffeomorphic image registration algorithm

http://library.utia.cas.cz/prace/20030125.pdf

Image registration methods: a survey

A novel approach to correcting for intensity nonuniformity in magnetic resonance (MR) data is described that achieves high performance without requiring a model of the tissue classes present. The method has the advantage that it can be applied at an early stage in an automated data analysis, before a tissue model is available. Described as nonparametric nonuniform intensity normalization (N3), the method is independent of pulse sequence and insensitive to pathological data that might otherwise violate model assumptions. To eliminate the dependence of the field estimate on anatomy, an iterative approach is employed to estimate both the multiplicative bias field and the distribution of the true tissue intensities. The performance of this method is evaluated using both real and simulated MR data.

/pdf/a-nonparametric-method-for-automatic-correction-of-intensity-4smqm7oz20.pdf

A nonparametric method for automatic correction of intensity nonuniformity in MRI data

Medical image registration is an important task in medical image processing. It refers to the process of aligning data sets, possibly from different modalities (e.g., magnetic resonance and computed tomography), different time points (e.g., follow-up scans), and/or different subjects (in case of population studies). A large number of methods for image registration are described in the literature. Unfortunately, there is not one method that works for all applications. We have therefore developed elastix, a publicly available computer program for intensity-based medical image registration. The software consists of a collection of algorithms that are commonly used to solve medical image registration problems. The modular design of elastix allows the user to quickly configure, test, and compare different registration methods for a specific application. The command-line interface enables automated processing of large numbers of data sets, by means of scripting. The usage of elastix for comparing different registration methods is illustrated with three example experiments, in which individual components of the registration method are varied.

elastix : A Toolbox for Intensity-Based Medical Image Registration

Respiratory motion during PET acquisition leads to blurring in images and quantification underestimation. We propose a practical, anatomy independent MR-based correction strategy for PET data affected by motion, and show it can improve image quality for both PET acquired simultaneously to the motion-capturing MR, and for PET acquired up to 1 hour earlier during a clinical scan. For our method, a short additional PET/MR sequence is acquired to form a patient-specific MR-based motion model, with a PET-derived respiratory signal and a gradient echo 2D multi-slice sequence. To evaluate our method, uncorrected and motion-corrected images are compared using line profiles, and quantitatively with SUV peak in avid lesions. We show that clinical PET image quality can be improved using only a short additional PET/MR acquisition with no external respiratory hardware, standard MR sequences and an open registration method.

Practical PET respiratory motion correction in clinical simultaneous PET/MR

This paper develops and analyzes the performance of an adaptive diffusion regularization method with a specific algorithm reconstruction method called the Lagged Diffusivity Newton-Krylov method for Diffuse Optical Tomography inverse problem.

Adaptive diffusion regularization method of inverse problem for Diffuse Optical Tomography

Methods which rely on the transmission of light through tissue are increasingly being used to study functional activation of the brain. To understand these measurements and to fully exploit the spatial information present in multi-channel recordings, optical image reconstruction is essential. In this chapter, we briefly review the methods for solving the forward and inverse problems which define the optical image reconstruction process.

Optical Image Reconstruction

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do not provide uncertainty on the obtained reconstruction. In this work, we develop a scalable, data-driven, knowledge-aided computational framework to quantify the model uncertainty via Bayesian neural networks. The approach builds on, and extends deep gradient descent, a recently developed greedy iterative training scheme, and recasts it within a probabilistic framework. Scalability is achieved by being hybrid in the architecture: only the last layer of each block is Bayesian, while the others remain deterministic, and by being greedy in training. The framework is showcased on one representative medical imaging modality, viz. computed tomography with either sparse view or limited view data, and exhibits competitive performance with respect to state-of-the-art benchmarks, e.g., total variation, deep gradient descent and learned primal-dual.

Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent

To improve the imaging performance of optical projection tomography (OPT) in live samples, we have explored a parallelized implementation of semi-confocal line illumination and detection to discriminate against scattered photons. Slice-illuminated OPT (sl-OPT) improves reconstruction quality in scattering samples by reducing interpixel crosstalk at the cost of increased acquisition time. For in vivo imaging, this can be ameliorated through the use of compressed sensing on angularly undersampled OPT data sets. Here, we demonstrate sl-OPT applied to 3D imaging of bead phantoms and live adult zebrafish.

Simon R. Arridge

Papers

Practical PET respiratory motion correction in clinical simultaneous PET/MR

Adaptive diffusion regularization method of inverse problem for Diffuse Optical Tomography

Optical Image Reconstruction

Quantifying Model Uncertainty in Inverse Problems via Bayesian Deep Gradient Descent

Slice-illuminated optical projection tomography.