Isotropic inverse-problem approach for two-dimensional phase unwrapping

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data-fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total-variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation

Visualization and Localization of Interventional Devices with MRI by Susceptibility Mapping

Recently, interventional procedures can be performed with the visual assistance of MRI. However, the devices used in these procedures, such as brachytherapy seeds, biopsy needles, markers, and stents, have a large magnetic susceptibility that leads to severe signal loss and distortion in the MRI images and degrades the accuracy of the localization. Right now, there is no effective way to correctly identify, localize and visualize these interventional devices in MRI images. In this dissertation, we proposed a method to improve the accuracy of localization and visualization by generating positive contrast of the interventional devices using a regularized L1 minimization algorithm. Specifically, the spin-echo sequence with a shifted 180-degree pulse is used to acquire high SNR data. A short shift time is used to avoid severe phase wrap. A phase unwrapping method based on Markov Random Field using Highest-Confidence-First algorithm is proposed to unwrap the phase image. Then the phase images with different shifted time are used to calculate the field map. Next, L1 regularized deconvolution is performed to calculate the susceptibility map. With much higher susceptibility of the interventional devices than the background tissue, the interventional devices show positive-contrast in the susceptibility image. Computer simulations were performed to study the effect of the signal-to-noise ratio, resolution, orientation and size of the interventional devices on the accuracy of the results. Experiments were performed using gelatin and tissue phantom with brachytherapy seeds, gelatin phantoms with platinum wires, and water phantom with titanium needles. The results show that the proposed method provide positive contrast images of these interventional devices, differentiate them from other structures in the MRI images, and improves the visualization and localization of the devices

Field Map Reconstruction in Magnetic Resonance Imaging Using Bayesian Estimation

Field inhomogeneities in Magnetic Resonance Imaging (MRI) can cause blur or image distortion as they produce off-resonance frequency at each voxel. These effects can be corrected if an accurate field map is available. Field maps can be estimated starting from the phase of multiple complex MRI data sets. In this paper we present a technique based on statistical estimation in order to reconstruct a field map exploiting two or more scans. The proposed approach implements a Bayesian estimator in conjunction with the Graph Cuts optimization method. The effectiveness of the method has been proven on simulated and real data

2D Phase Unwrapping via Graph Cuts

Phase imaging technologies such as interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI), or optical interferometry, are nowadays widespread and with an increasing usage. The so-called phase unwrapping, which consists in the in- ference of the absolute phase from the modulo-2π phase, is a critical step in many of their processing chains, yet still one of its most challenging problems. We introduce an en- ergy minimization based approach to 2D phase unwrapping. In this approach we address the problem by adopting a Bayesian point of view and a Markov random field (MRF) to model the phase. The maximum a posteriori estimation of the absolute phase gives rise to an integer optimization problem, for which we introduce a family of efficient algo- rithms based on existing graph cuts techniques. We term our approach and algorithms PUMA, for Phase Unwrapping MAx flow. As long as the prior potential of the MRF is convex, PUMA guarantees an exact global solution. In particular it solves exactly all the minimum L p norm (p ≥ 1) phase unwrapping problems, unifying in that sense, a set of existing independent algorithms. For non convex potentials we introduce a version of PUMA that, while yielding only approximate solutions, gives very useful phase unwrap- ping results. The main characteristic of the introduced solutions is the ability to blindly preserve discontinuities. Extending the previous versions of PUMA, we tackle denoising by exploiting a multi-precision idea, which allows us to use the same rationale both for phase unwrapping and denoising. Finally, the last presented version of PUMA uses a frequency diversity concept to unwrap phase images having large phase rates. A representative set of experiences illustrates the performance of PUMA

Towards efficient neurosurgery: Image analysis for interventional MRI

Interventional magnetic resonance imaging (iMRI) is being increasingly used for performing imageguided neurosurgical procedures. Intermittent imaging through iMRI can help a neurosurgeon visualise the target and eloquent brain areas during neurosurgery and lead to better patient outcome. MRI plays an important role in planning and performing neurosurgical procedures because it can provide highresolution anatomical images that can be used to discriminate between healthy and diseased tissue, as well as identify location and extent of functional areas. This is of significant clinical utility as it helps the surgeons maximise target resection and avoid damage to functionally important brain areas. There is clinical interest in propagating the pre-operative surgical information to the intra-operative image space as this allows the surgeons to utilise the pre-operatively generated surgical plans during surgery. The current state of the art neuronavigation systems achieve this by performing rigid registration of pre-operative and intra-operative images. As the brain undergoes non-linear deformations after craniotomy (brain shift), the rigidly registered pre-operative images do not accurately align anymore with the intra-operative images acquired during surgery. This limits the accuracy of these neuronavigation systems and hampers the surgeon’s ability to perform more aggressive interventions. In addition, intra-operative images are typically of lower quality with susceptibility artefacts inducing severe geometric and intensity distortions around areas of resection in echo planar MRI images, significantly reducing their utility in the intraoperative setting. This thesis focuses on development of novel methods for an image processing workflow that aims to maximise the utility of iMRI in neurosurgery. I present a fast, non-rigid registration algorithm that can leverage information from both structural and diffusion weighted MRI images to localise target lesions and a critical white matter tract, the optic radiation, during surgical management of temporal lobe epilepsy. A novel method for correcting susceptibility artefacts in echo planar MRI images is also developed, which combines fieldmap and image registration based correction techniques. The work developed in this thesis has been validated and successfully integrated into the surgical workflow at the National Hospital for Neurology and Neurosurgery in London and is being clinically used to inform surgical decisions

Contributions of Continuous Max-Flow Theory to Medical Image Processing

Discrete graph cuts and continuous max-flow theory have created a paradigm shift in many areas of medical image processing. As previous methods limited themselves to analytically solvable optimization problems or guaranteed only local optimizability to increasingly complex and non-convex functionals, current methods based now rely on describing an optimization problem in a series of general yet simple functionals with a global, but non-analytic, solution algorithms. This has been increasingly spurred on by the availability of these general-purpose algorithms in an open-source context. Thus, graph-cuts and max-flow have changed every aspect of medical image processing from reconstruction to enhancement to segmentation and registration. To wax philosophical, continuous max-flow theory in particular has the potential to bring a high degree of mathematical elegance to the field, bridging the conceptual gap between the discrete and continuous domains in which we describe different imaging problems, properties and processes. In Chapter 1, we use the notion of infinitely dense and infinitely densely connected graphs to transfer between the discrete and continuous domains, which has a certain sense of mathematical pedantry to it, but the resulting variational energy equations have a sense of elegance and charm. As any application of the principle of duality, the variational equations have an enigmatic side that can only be decoded with time and patience. The goal of this thesis is to show the contributions of max-flow theory through image enhancement and segmentation, increasing incorporation of topological considerations and increasing the role played by user knowledge and interactivity. These methods will be rigorously grounded in calculus of variations, guaranteeing fuzzy optimality and providing multiple solution approaches to addressing each individual problem

Interferometric Synthetic Aperture Sonar Signal Processing for Autonomous Underwater Vehicles Operating Shallow Water

The goal of the research was to develop best practices for image signal processing method for InSAS systems for bathymetric height determination. Improvements over existing techniques comes from the fusion of Chirp-Scaling a phase preserving beamforming techniques to form a SAS image, an interferometric Vernier method to unwrap the phase; and confirming the direction of arrival with the MUltiple SIgnal Channel (MUSIC) estimation technique. The fusion of Chirp-Scaling, Vernier, and MUSIC lead to the stability in the bathymetric height measurement, and improvements in resolution. This method is computationally faster, and used less memory then existing techniques

Simplified Post Processing of Cine DENSE Cardiovascular Magnetic Resonance for Quantification of Cardiac Mechanics

BACKGROUND: Cardiovascular magnetic resonance using displacement encoding with stimulated echoes (DENSE) is capable of assessing advanced measures of cardiac mechanics such as strain and torsion. A potential hurdle to widespread clinical adoption of DENSE is the time required to manually segment the myocardium during post-processing of the images. To overcome this hurdle, we proposed a radical approach in which only three contours per image slice are required for post-processing (instead of the typical 30-40 contours per image slice). We hypothesized that peak left ventricular circumferential, longitudinal and radial strains and torsion could be accurately quantified using this simplified analysis. METHODS AND RESULTS: We tested our hypothesis on a large multi-institutional dataset consisting of 541 DENSE image slices from 135 mice and 234 DENSE image slices from 62 humans. We compared measures of cardiac mechanics derived from the simplified post-processing to those derived from original post-processing utilizing the full set of 30-40 manually-defined contours per image slice. Accuracy was assessed with Bland-Altman limits of agreement and summarized with a modified coefficient of variation. The simplified technique showed high accuracy with all coefficients of variation less than 10% in humans and 6% in mice. The accuracy of the simplified technique was also superior to two previously published semi-automated analysis techniques for DENSE post-processing. CONCLUSIONS: Accurate measures of cardiac mechanics can be derived from DENSE cardiac magnetic resonance in both humans and mice using a simplified technique to reduce post-processing time by approximately 94%. These findings demonstrate that quantifying cardiac mechanics from DENSE data is simple enough to be integrated into the clinical workflow