Peter Renaud

Reducing beam hardening effects and metal artefacts in spectral CT using Medipix3RX

This paper discusses methods for reducing beam hardening effects and metal artefacts using spectral x-ray information in biomaterial samples. A small-animal spectral scanner was operated in the 15 to 80 keV x-ray energy range for this study. We use the photon-processing features of a CdTe-Medipix3RX ASIC in charge summing mode to reduce beam hardening and associated artefacts. We present spectral data collected for metal alloy samples, its analysis using algebraic 3D reconstruction software and volume visualisation using a custom volume rendering software. The cupping effect and streak artefacts are quantified in the spectral datasets. The results show reduction in beam hardening effects and metal artefacts in the narrow high energy range acquired using the spectroscopic detector. A post-reconstruction comparison between CdTe-Medipix3RX and Si-Medipix3.1 is discussed. The raw data and processed data are made available (http://hdl.handle.net/10092/8851) for testing with other software routines.This paper discusses methods for reducing beam hardening effects using spectral data for biomaterial applications. A small-animal spectral scanner operating in the diagnostic energy range was used. We investigate the use of photon-processing features of the Medipix3RX ASIC in reducing beam hardening and associated artefacts. A fully operational charge summing mode was used during the imaging routine. We present spectral data collected for metal alloy samples, its analysis using algebraic 3D reconstruction software and volume visualisation using a custom volume rendering software. Narrow high energy acquisition using the photon-processing detector revealed substantial reduction in beam hardening effects and metal artefacts.

MARS spectral molecular imaging of lamb tissue: data collection and image analysis

Spectral molecular imaging is a new imaging technique able to discriminate and quantify different components of tissue simultaneously at high spatial and high energy resolution. Our MARS scanner is an x-ray based small animal CT system designed to be used in the diagnostic energy range (20–140 keV). In this paper, we demonstrate the use of the MARS scanner, equipped with the Medipix3RX spectroscopic photon-processing detector, to discriminate fat, calcium, and water in tissue. We present data collected from a sample of lamb meat including bone as an illustrative example of human tissue imaging. The data is analyzed using our 3D Algebraic Reconstruction Algorithm (MARS-ART) and by material decomposition based on a constrained linear least squares algorithm. The results presented here clearly show the quantification of lipid-like, water-like and bone-like components of tissue. However, it is also clear to us that better algorithms could extract more information of clinical interest from our data. Because we are one of the first to present data from multi-energy photon-processing small animal CT systems, we make the raw, partial and fully processed data available with the intention that others can analyze it using their familiar routines. The raw, partially processed and fully processed data of lamb tissue along with the phantom calibration data can be found at http://hdl.handle.net/10092/8531.

Efficient frequency-domain sample selection for recovering limited-support images

An image whose region of support is smaller than its bounding rectangle can, in principle, be reconstructed from a subset of the Nyquist samples. However, determining such a sampling set that gives a stable reconstruction is a difficult and computationally intensive problem. An algorithm is developed for determining periodic nonuniform sampling patterns that is orders of magnitude faster than existing algorithms. The speedup is achieved by using a sequential selection algorithm and heuristic metrics for the quality of sampling sets that are fast to compute, as opposed to the more rigorous linear algebraic metrics that have been used previously. Simulations show that the sampling sets determined using the new algorithm give image reconstructions that are of accuracy comparable with those determined by other slower algorithms.

Preliminary experimental results from a MARS Micro-CT system

The Medipix All Resolution System (MARS) system is a commercial spectral/multi-energy micro-CT scanner designed and assembled by the MARS Bioimaging, Ltd. in New Zealand. This system utilizes the state-of-the-art Medipix photon-counting, energy-discriminating detector technology developed by a collaboration at European Organization for Nuclear Research (CERN). In this paper, we report our preliminary experimental results using this system, including geometrical alignment, photon energy characterization, protocol optimization, and spectral image reconstruction. We produced our scan datasets with a multi-material phantom, and then applied ordered subset-simultaneous algebraic reconstruction technique (OS-SART) to reconstruct images in different energy ranges and principal component analysis (PCA) to evaluate spectral deviation among the energy ranges.

Determinant and Exchange Algorithms for Observation Subset Selection

In many applications involving image reconstruction, signal observation time is limited. This emphasizes the requirement for optimal observation selection algorithms. A selection criterion using the trace of a matrix forms the basis of two existing algorithms, the Sequential Backward Selection and Sequential Forward Selection algorithms. Neither is optimal although both generally perform well. Here we introduce a trace row-exchange criterion to further improve the quality of the selected subset and introduce another observation selection criterion based upon the determinant of a matrix.

THE STABILIZED POINCARE–HEISENBERG ALGEBRA: A CLIFFORD ALGEBRA VIEWPOINT

2000) Abstract. The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after attempting to combine the Lie algebras of quantum mechanics and relativity which by themselves are stable, however not when combined. In this paper we show how the sixteen dimensional Clifford algebra Cl(1,3) can be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional stability considerations, relying instead on the fact that Cl(1,3) is a semi-simple algebra and therefore stable. It is therefore conceptually easier and more straightforward to work with a Clifford algebra. The Clifford algebra path suggests the next evolutionary step toward a theory of physics at the interface of GR and QM might be to depart from working in space-time and instead to work in space-time-momentum.

A box constrained gradient projection algorithm for compressed sensing

A new algorithm is presented which aims to solve problems from compressed sensing - under-determined problems where the solution vector is known a priori to be sparse. Upper bounds on the solution vector are found so that the problem can be reformulated as a box-constrained quadratic programme. A sparse solution is sought using a Barzilai-Borwein type projection algorithm. New insight into the choice of step length is provided through a study of the special structure of the underlying problem together with upper bounds on the step length. Numerical experiments are conducted and results given, comparing this algorithm with a number of other current algorithms.

MARS-MD: Rejection based image domain material decomposition

This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the under-determined problem where there are more materials than energy bins. This heuristic contains three parts: (1) splitting the problem into a number of possible sub-problems, each containing fewer materials; (2) solving each sub-problem; and (3) applying rejection criteria to eliminate all but one sub-problems solution. An advantage of this process is that different constraints can be applied to each sub-problem if necessary. In addition, the result of this process is that solutions will be sparse in the material domain, which reduces crossover of signal between material images. Two algorithms based on this process are presented: the Segmentation variant, which uses segmented material classes to define each sub-problem; and the Angular Rejection variant, which defines the rejection criteria using the angle between reconstructed attenuation vectors.

Segmentation enhances material analysis in multi-energy CT: A simulation study

A segmentation algorithm that assists material analysis in multi-energy computed tomography is presented. Segmentation is typically used in conjunction with quantitative material analysis algorithms (known as material decomposition) to increase the total number of materials which can be discriminated and quantified. The algorithm illustrated here identifies voxels (in the image domain) with one of three material classes: air, soft tissues and dense tissue or contrast pharmaceuticals. Two soft tissue materials are chosen (the most and the least attenuating soft tissues) to define the boundaries between the different material classes. The intensity (calculated from the multi-energy representation using the Euclidean norm) of each voxel is compared to the two boundary materials to determine which material class it belongs to. Unlike other intensity based segmentation methods this algorithm checks, using multi-variate confidence intervals (ellipsoids), whether each voxel is statistically distinguishable from the two boundary materials. If the voxels are not distinguishable then they are defaulted to the soft tissue class. An advantage of this segmentation method is that noise which passes through to the binary representations of each material class typically resemble salt and pepper noise, which is easily removed with a median filter. Simulations demonstrate that the algorithm can correctly allocate a variety of medically relevant soft tissue and non soft tissue materials to their correct material classes and that segmentation using multi-energy information can handle noisier data than when using single-energy information. The proposed algorithm is also successfully applied to a multi-energy CT scan taken using the MARS (Medipix All Resolution System) scanner.

X-ray image enhancement via determinant based feature selection.

Previous work has investigated the feasibility of using Eigenimage-based enhancement tools to highlight abnormalities on chest X-rays (Butler et al in J Med Imaging Radiat Oncol 52:244–253, 2008). While promising, this approach has been limited by computational restrictions of standard clinical workstations, and uncertainty regarding what constitutes an adequate sample size. This paper suggests an alternative mathematical model to the above referenced singular value decomposition method, which can significantly reduce both the required sample size and the time needed to perform analysis. Using this approach images can be efficiently separated into normal and abnormal parts, with the potential for rapid highlighting of pathology.