Calibration Using Matrix Completion with Application to Ultrasound Tomography

We study the calibration process in circular ultrasound tomography devices where the sensor positions deviate from the circumference of a perfect circle. This problem arises in a variety of applications in signal processing ranging from breast imaging to sensor network localization. We introduce a novel method of calibration/localization based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can easily estimate the sensor positions using multi-dimensional scaling (MDS) method. In practice however, due to the transitional behaviour of the sensors and the beam form of the transducers, the ToF measurements for close-by sensors are unavailable. Further, random malfunctioning of the sensors leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we incorporate the fact that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate the missing ToFs, we apply a state-of-the-art low-rank matrix completion algorithm, OPTSPACE . To find the correct positions of the sensors (our ultimate goal) we then apply MDS. We show analytic bounds on the overall error of the whole process in the presence of noise and hence deduce its robustness. Finally, we confirm the functionality of our method in practice by simulations mimicking the measurements of a circular ultrasound tomography device.Comment: submitted to IEEE Transaction on Signal Processin

An open environment CT-US fusion for tissue segmentation during interventional guidance.

Therapeutic ultrasound (US) can be noninvasively focused to activate drugs, ablate tumors and deliver drugs beyond the blood brain barrier. However, well-controlled guidance of US therapy requires fusion with a navigational modality, such as magnetic resonance imaging (MRI) or X-ray computed tomography (CT). Here, we developed and validated tissue characterization using a fusion between US and CT. The performance of the CT/US fusion was quantified by the calibration error, target registration error and fiducial registration error. Met-1 tumors in the fat pads of 12 female FVB mice provided a model of developing breast cancer with which to evaluate CT-based tissue segmentation. Hounsfield units (HU) within the tumor and surrounding fat pad were quantified, validated with histology and segmented for parametric analysis (fat: -300 to 0 HU, protein-rich: 1 to 300 HU, and bone: HU>300). Our open source CT/US fusion system differentiated soft tissue, bone and fat with a spatial accuracy of ∼1 mm. Region of interest (ROI) analysis of the tumor and surrounding fat pad using a 1 mm(2) ROI resulted in mean HU of 68±44 within the tumor and -97±52 within the fat pad adjacent to the tumor (p<0.005). The tumor area measured by CT and histology was correlated (r(2) = 0.92), while the area designated as fat decreased with increasing tumor size (r(2) = 0.51). Analysis of CT and histology images of the tumor and surrounding fat pad revealed an average percentage of fat of 65.3% vs. 75.2%, 36.5% vs. 48.4%, and 31.6% vs. 38.5% for tumors <75 mm(3), 75-150 mm(3) and >150 mm(3), respectively. Further, CT mapped bone-soft tissue interfaces near the acoustic beam during real-time imaging. Combined CT/US is a feasible method for guiding interventions by tracking the acoustic focus within a pre-acquired CT image volume and characterizing tissues proximal to and surrounding the acoustic focus

Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption\ud

We present a ‘hybrid’ imaging approach which can image both light absorption properties and acoustic transmission properties of an object in a two-dimensional slice using a computed tomography (CT) photoacoustic imager. The ultrasound transmission measurement method uses a strong optical absorber of small cross-section placed in the path of the light illuminating the sample. This absorber, which we call a passive element acts as a source of ultrasound. The interaction of ultrasound with the sample can be measured in transmission, using the same ultrasound detector used for photoacoustics. Such measurements are made at various angles around the sample in a CT approach. Images of the ultrasound propagation parameters, attenuation and speed of sound, can be reconstructed by inversion of a measurement model. We validate the method on specially designed phantoms and biological specimens. The obtained images are quantitative in terms of the shape, size, location, and acoustic properties of the examined heterogeneitie

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine - change of title in the last revisio

In vivo measurement of human brain elasticity using a light aspiration device

The brain deformation that occurs during neurosurgery is a serious issue impacting the patient "safety" as well as the invasiveness of the brain surgery. Model-driven compensation is a realistic and efficient solution to solve this problem. However, a vital issue is the lack of reliable and easily obtainable patient-specific mechanical characteristics of the brain which, according to clinicians' experience, can vary considerably. We designed an aspiration device that is able to meet the very rigorous sterilization and handling process imposed during surgery, and especially neurosurgery. The device, which has no electronic component, is simple, light and can be considered as an ancillary instrument. The deformation of the aspirated tissue is imaged via a mirror using an external camera. This paper describes the experimental setup as well as its use during a specific neurosurgery. The experimental data was used to calibrate a continuous model. We show that we were able to extract an in vivo constitutive law of the brain elasticity: thus for the first time, measurements are carried out per-operatively on the patient, just before the resection of the brain parenchyma. This paper discloses the results of a difficult experiment and provide for the first time in-vivo data on human brain elasticity. The results point out the softness as well as the highly non-linear behavior of the brain tissue.Comment: Medical Image Analysis (2009) accept\'

Single-shot hybrid photoacoustic-fluorescent microendoscopy through a multimode fiber with wavefront shaping

We present a minimally-invasive endoscope based on a multimode fiber that combines photoacoustic and fluorescence sensing. From the measurement of a transmission matrix during a prior calibration step, a focused spot is produced and raster-scanned over a sample at the distal tip of the fiber by use of a fast spatial light modulator. An ultra-sensitive fiber-optic ultrasound sensor for photoacoustic detection placed next to the fiber is combined with a photodetector to obtain both fluorescence and photoacoustic images with a distal imaging tip no larger than 250 µm. The high signal-to-noise ratio provided by wavefront shaping based focusing and the ultra-sensitive ultrasound sensor enables imaging with a single laser shot per pixel, demonstrating fast two-dimensional hybrid in vitro imaging of red blood cells and fluorescent beads

CALIBRATION OF AN ULTRASONIC TRANSMISSIVE COMPUTED TOMOGRAPHY SYSTEM

Tato dizertace je zaměřena na medicínskou zobrazovací modalitu – ultrazvukovou počítačovou tomografii – a algoritmy zlepšující kvalitu zobrazení, zejména kalibraci USCT přístroje. USCT je novou modalitou kombinující ultrazvukový přenos signálů a principy tomografické rekonstrukce obrazů vyvíjených pro jiné tomografické systémy. V principu lze vytvořit kvantitativní 3D obrazové objemy s vysokým rozlišením a kontrastem. USCT je primárně určeno pro diagnózu rakoviny prsu. Autor spolupracoval na projektu Institutu Zpracování dat a Elektroniky, Forschungszentrum Karlsruhe, kde je USCT systém vyvíjen. Jeden ze zásadních problémů prototypu USCT v Karlsruhe byla absence kalibrace. Tisíce ultrazvukových měničů se liší v citlivosti, směrovosti a frekvenční odezvě. Tyto parametry jsou navíc proměnné v čase. Další a mnohem závažnější problém byl v pozičních odchylkách jednotlivých měničů. Všechny tyto aspekty mají vliv na konečnou kvalitu rekonstruovaných obrazů. Problém kalibrace si autor zvolil jako hlavní téma dizertace. Tato dizertace popisuje nové metody v oblastech rekonstrukce útlumových obrazů, kalibrace citlivosti měničů a zejména geometrická kalibrace pozic měničů. Tyto metody byly implementovány a otestovány na reálných datech pocházejících z prototypu USCT z Karlsruhe.This dissertation is centered on a medical imaging modality – the ultrasonic computed tomography (USCT) – and algorithms which improve the resulting image quality, namely the calibration of a USCT device. The USCT is a novel imaging modality which combines the phenomenon of ultrasound and image reconstruction principles developed for other tomographic systems. It is capable of producing quantitative 3D image volumes with high resolution and tissue contrast and is primarily aimed at breast cancer diagnosis. The author was involved in a joint research project at the Institute of Data Processing and Electronics, Forschungszentrum Karlsruhe (German National Research Center), where a USCT system is being developed. One of the main problems in the Karlsruhe USCT prototype was the absence of any calibration. The thousands of transducers used in the system have deviations in sensitivity, directivity, and frequency response. These parameters change over time as the transducers age. Also the mechanical positioning of the transducer elements is not precise. All these aspects greatly affect the overall quality of the reconstructed images. The problem of calibration of a USCT system was chosen as the main topic for this dissertation. The dissertation thesis presents novel methods in the area of reconstruction of attenuation images, sensitivity calibration, and mainly geometrical calibration. The methods were implemented and tested on real data generated by the Karlsruhe USCT device.