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

This thesis describes the development of a computer graphics facility, referred to as UCL3D, for the planning, simulation and evaluation of Maxillo-Facial surgery on a conventional super-minicomputer, with a colour graphics framestore. The introduction defines the requirements as data acquisition, preprocessing, visualisation, dissection, manipulation, quantification, and registration. The principle innovations are in the visualisation, dissection and manipulation stages. The first part of the thesis is concerned with basic definitions and a review of other work. The data acquisition is assumed to be from a medical imaging device that produces a 3D digital array of density values. The preprocessing stage involves interpolation, artefact removal, subregioning, and segmentation. The computer representation of discrete objects from medical 3D data is discussed, and the need to have a volume based representation is justified. The implementation of UCL3D is in terms of octrees, although the principles could be applied to other representations. Both a binary and grey-value implementation have been developed, and for each case, a new structure variation is described. Visualisation is discussed in terms of these representations and surface shading techniques appropriate to each are introduced. A new algorithm for deriving the quadtree projection of an octree in orthogonal directions is presented, and its advantages explained. The concept of a general volume mask, specified interactively, is introduced for the dissection problem. The space partitioning resulting from this mask is more general than previous methods. Manipulation is considered as the combination of Boolean operations and translation and rotations, acting on combinations of dissected objects. The philosophy is to cut and merge medical objects to simulate the "osteotomies" encountered in surgery. Boolean expressions of objects may be visualised prior to being created. A description of the application of the system to several clinical cases is given and finally several areas for future work are suggested.

Data structures and algorithms for manipulation and display in computer simulated surgery

The photoacoustic image reconstruction problem (inverse problem) is to estimate an initial acoustic pressure distribution from measurements of ultrasound waves generated within an object due to optical excitation with a short light pulse. In this work, the recently suggested Bayesian approach to photoacoustic tomography is extended to three dimensions and an iterative matrix-free method for the solution of the problem is described. Image reconstruction is investigated with numerical simulations and experimental data. The use of different prior information and noise models in different sensor geometries, including a limited-view setup, is investigated. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution even in a limited-view setup provided that prior information and the noise have been properly modelled.

/pdf/photoacoustic-image-reconstruction-in-bayesian-framework-11pihdfz5i.pdf

Photoacoustic image reconstruction in Bayesian framework

In this paper we propose a novel method for collimator design in single photon emission tomography (SPECT) The challenge here is to find a practical collimator design that allows good recovery and good sensitivity Instead of working on the collimator's shape, the problem is addressed by optimizing the point spread function (PSF) with respect to the performance of the reconstruction algorithm in terms of resolution modelling The optimization is based on an object-dependent cost function that takes into account bother recovery coefficient (RC) and sensitivity Therefore, for each object considered a different "optimal" PSF is expected Once a PSF is obtained, we assess its performances by plotting the coefficient of variation (COV) versus the recovery coefficient (RC) at each iteration of a maximum likelihood maximization expectation (MLEM) algorithm We performed our experiments on two-dimensional (2-D) geometric phantoms, in order to investigate the relationship between the optimal PSF and the object geometrical properties, as well as on a 2-D brain activity phantom We show that the optimized PSF's lead to resolution models that improve both image resolution and signal to noise ratio

Point spread function optimization in SPECT

Diffuse optical tomography (DOT) is a functional imaging modality which aims to retrieve the optical characteristics of the probed tissue, namely light absorption and diffusion. The accurate retrieval of the spatial distribution for each optical characteristic involves the solution of a highly-ill posed, non-linear inverse problem, thus employing a regularization is essential. In this work, we propose an entropic regularization scheme for DOT reconstruction that uses a priori structural information through mutual information (MI) and joint entropy (JE).We compare MI and JE through simulations that illustrate their behavior when the reference and DOT images are not identical in structure. We propose an efficient implementation of these regularizers based on fast Fourier transforms. The method is tested through numerical simulations.

Diffusion optical tomography using entropic priors

Simultaneous PET and MR acquisitions have now become possible with the new hybrid Biograph Molecular MR (mMR) scanner from Siemens. The purpose of this work is to create a platform for mMR 3D and 4D PET image reconstruction which would be freely accessible to the community as well as fully adjustable in order to obtain optimal images for a given research task in PET imaging. The proposed platform is envisaged to prove useful in developing novel and robust image bio-markers which could then be adapted for use on the mMR scanner.

STIR (Software for Tomographic Image Reconstruction [1]), an open source C++ library, has been used as a basis for this platform. However, a number of practical issues have to be addressed before useful reconstructed images can be obtained. Many of the practical issues have been addressed and reconstructions of two datasets (phantom and human brain) are demonstrated.


The reconstruction pipeline involves the following:


Conversion of the Siemens Dicom files to the STIR interfile format.


Histogramming the emission data.


Component-based normalisation.


Estimation and correction for attenuation and scatter using atlas based µ-maps [2].


Correction for randoms.


Iterative image reconstruction ([3–5]).




Two datasets were used: uniform cylinder phantom and FDG-PET human brain scan. Figure ​Figure11 shows the OSEM reconstruction using the of-line version of the Siemens Healthcare reconstruction software which was made available for this project (top); the STIR reconstruction (middle); and the µ-map including the bed component (bottom).



Figure 1

Image reconstruction of the phantom using Siemens proprietary software (top) and STIR (middle). Bottom: the MRI derived µ-map.



The reconstruction of the FDG human brain dataset is presented in Figure ​Figure22 using Siemens proprietary software (top) and the proposed STIR pipeline (bottom).



Figure 2

Image reconstruction of the human brain FDG-PET dataset using Siemens proprietary software (top) and STIR (bottom).



It was demonstrated that STIR image reconstruction of PET mMR data is possible paving the way to more advanced models included in the pipeline of 4D PET reconstruction.

/pdf/image-reconstruction-of-mmr-pet-data-using-the-open-source-2acosxqrux.pdf

Simon R. Arridge

Papers

Data structures and algorithms for manipulation and display in computer simulated surgery

Photoacoustic image reconstruction in Bayesian framework

Point spread function optimization in SPECT

Diffusion optical tomography using entropic priors

Image reconstruction of mMR PET data using the open source software STIR