Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Simultaneous multislice acquisition with multi-contrast segmented EPI for separation of signal contributions in dynamic contrast-enhanced imaging

We present a method to efficiently separate signal in magnetic resonance imaging (MRI) into a base signal S0, representing the mainly T1-weighted component without T2*-relaxation, and its T2*-weighted counterpart by the rapid acquisition of multiple contrasts for advanced pharmacokinetic modelling. This is achieved by incorporating simultaneous multislice (SMS) imaging into a multi-contrast, segmented echo planar imaging (EPI) sequence to allow extended spatial coverage, which covers larger body regions without time penalty. Simultaneous acquisition of four slices was combined with segmented EPI for fast imaging with three gradient echo times in a preclinical perfusion study. Six female domestic pigs, German-landrace or hybrid-form, were scanned for 11 minutes respectively during administration of gadolinium-based contrast agent. Influences of reconstruction methods and training data were investigated. The separation into T1- and T2*-dependent signal contributions was achieved by fitting a standard analytical model to the acquired multi-echo data. The application of SMS yielded sufficient temporal resolution for the detection of the arterial input function in major vessels, while anatomical coverage allowed perfusion analysis of muscle tissue. The separation of the MR signal into T1- and T2*-dependent components allowed the correction of susceptibility related changes. We demonstrate a novel sequence for dynamic contrast-enhanced MRI that meets the requirements of temporal resolution (Δt < 1.5 s) and image quality. The incorporation of SMS into multi-contrast, segmented EPI can overcome existing limitations of dynamic contrast enhancement and dynamic susceptibility contrast methods, when applied separately. The new approach allows both techniques to be combined in a single acquisition with a large spatial coverage

Simultaneous Multislice (SMS) Imaging Techniques

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High-resolution diffusion-weighted brain MRI under motion

Magnetic resonance imaging is one of the fastest developing medical imaging techniques. It provides excellent soft tissue contrast and has been a leading tool for neuroradiology and neuroscience research over the last decades. One of the possible MR imaging contrasts is the ability to visualize diffusion processes. The method, referred to as diffusion-weighted imaging, is one of the most common clinical contrasts but is prone to artifacts and is challenging to acquire at high resolutions. This thesis aimed to improve the resolution of diffusion weighted imaging, both in a clinical and in a research context. While diffusion-weighted imaging traditionally has been considered a 2D technique the manuscripts and methods presented here explore 3D diffusion acquisitions with isotropic resolution. Acquiring multiple small 3D volumes, or slabs, which are combined into one full volume has been the method of choice in this work. The first paper presented explores a parallel imaging driven multi-echo EPI readout to enable high resolution with reduced geometric distortions. The work performed on diffusion phase correction lead to an understanding that was used for the subsequent multi-slab papers. The second and third papers introduce the diffusion-weighted 3D multi-slab echo-planar imaging technique and explore its advantages and performance. As the method requires a slightly increased acquisition time the need for prospective motion correction became apparent. The forth paper suggests a new motion navigator using the subcutaneous fat surrounding the skull for rigid body head motion estimation, dubbed FatNav. The spatially sparse representation of the fat signal allowed for high parallel imaging acceleration factors, short acquisition times, and reduced geometric distortions of the navigator. The fifth manuscript presents a combination of the high-resolution 3D multi-slab technique and a modified FatNav module. Unlike our first FatNav implementation, using a single sagittal slab, this modified navigator acquired orthogonal projections of the head using the fat signal alone. The combined use of both presented methods provides a promising start for a fully motion corrected high-resolution diffusion acquisition in a clinical setting

Time-efficient and flexible design of optimized multishell HARDI diffusion

Purpose: Advanced diffusion magnetic resonance imaging benefits from collecting as much data as is feasible but is highly sensitive to subject motion and the risk of data loss increases with longer acquisition times. Our purpose was to create a maximally time-efficient and flexible diffusion acquisition capability with built-in robustness to partially acquired or interrupted scans. Our framework has been developed for the developing Human Connectome Project, but different application domains are equally possible. Methods: Complete flexibility in the sampling of diffusion space combined with free choice of phase-encode-direction and the temporal ordering of the sampling scheme was developed taking into account motion robustness, internal consistency, and hardware limits. A split-diffusion-gradient preparation, multiband acceleration, and a restart capacity were added. Results: The framework was used to explore different parameters choices for the desired high angular resolution diffusion imaging diffusion sampling. For the developing Human Connectome Project, a high-angular resolution, maximally time-efficient (20 min) multishell protocol with 300 diffusion-weighted volumes was acquired in >400 neonates. An optimal design of a high-resolution (1.2 × 1.2 mm2) two-shell acquisition with 54 diffusion weighted volumes was obtained using a split-gradient design. Conclusion: The presented framework provides flexibility to generate time-efficient and motion-robust diffusion magnetic resonance imaging acquisitions taking into account hardware constraints that might otherwise result in sub-optimal choices. Magn Reson Med, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes

HYPERPOLARIZED CARBON-13 MAGNETIC RESONANCE MEASUREMENTS OF TISSUE PERFUSION AND METABOLISM

Hyperpolarized Magnetic Resonance Imaging (HP MRI) is an emerging modality that enables non-invasive interrogation of cells and tissues with unprecedented biochemical detail. This technology provides rapid imaging measurements of the activity of a small quantity of molecules with a strongly polarized nuclear magnetic moment. This polarization is created in a polarizer separate from the imaging magnet, and decays continuously towards a non-detectable thermal equilibrium once the imaging agent is removed from the polarizer and administered by intravenous injection. Specialized imaging strategies are therefore needed to extract as much information as possible from the HP signal during its limited lifetime. In this work, we present innovative strategies for measurement of tissue perfusion and metabolism with HP MRI. These techniques include the capacity to sensitize the imaging signal to the diffusive motion of HP molecules, providing improved accuracy and reproducibility for assessment of agent uptake in tissue. The proposed methods were evaluated in numerical simulations, implemented on a preclinical MRI system and demonstrated in vivo in rodents through imaging of HP 13C urea. Using the simulation and imaging infrastructure developed in this work, established methods for encoding HP chemical signals were compared quantitatively. Lastly, our method was adapted for imaging of [2-13C]dihydroxyacetone, a novel HP agent that probes enzymatic flux through multiple biochemical pathways in vivo. Our results demonstrate the capacity of HP MRI to measure tissue perfusion and metabolism in ways not possible with the imaging modalities currently available in the clinic. As the use of HP MRI advances in clinical investigations of human disease, these imaging measurements can offer real-time and individualized information on disease states for early detection and therapeutic guidance

Subsampling receivers with applications to software defined radio systems

Este trabajo de tesis propone la utilización sistemas basados en submuestreo como una alternativa para la implementación de la etapa de down-conversion de los receptores de radio frecuencia (RF) empleados para aplicaciones multi-estándar y SDR (Software Defined Radio). El objetivo principal será el de optimizar el diseño en cuanto a flexibilidad y simplicidad, las cuales son propiedades inherentes en los sistemas basados en submuestreo. Por tanto, como reducir el número de componentes al mínimo es clave cuando un mismo receptor procesa diferentes estándares de comunicación, las arquitecturas basadas en submuestreo han sido seleccionadas, donde la reusabilidad de los componentes empleados es posible, así como la reducción de los costes totales de los receptores de comunicación y de los equipos de certificación que emplean estas arquitecturas. Un motivo adicional por el que los sistemas basados en submuestreo han sido seleccionados es el concerniente a la topología del receptor. Como la idea de la tecnología SDR es implementar todas las funcionalidades del receptor (filtrado, amplificación) en el dominio digital, el convertidores analógico-digital (ADC) deberá estar localizado en la cadena de recepción lo más cerca posible a la antena, siendo el objetivo final el convertir la señal directamente de RF a digital. Sin embargo, con los actuales ADC no es posible implementar esta idea debido al alto ancho de banda que necesitarían sin perder resolución para cubrir las especificaciones de los estándares de comunicaciones inalámbricas. Por tanto, los sistemas basados en submuestreo se presentan como la opción más adecuada para implementar este tipo de sistemas debido a que pueden muestrear la señal de entrada por debajo de la tasa de Nyquist, si se cumplen ciertas restricciones en cuanto a la elección de la frecuencia de muestreo. De este modo, los requerimientos del ADC serán relajados ya que, usando estas arquitecturas, este componente procesará la señal a frecuencias intermedias. Una vez se han introducido los conceptos principales de las técnicas de submuestreo, esta tesis doctoral presenta el diseño de una tarjeta de adquisición de datos basada en submuestreo con la finalidad de ser implementada como un receptor de test y certificación de banda ancha. El sistema propuesto proporciona una alta resolución para un elevado ancho de banda, a partir del uso de un S&H de bajo jitter y de un convertidor analógico digital ADC que trabaja a frecuencias intermedias. El sistema es implementado usando dispositivos comerciales en una placa de circuito impreso diseñada y fabricada, y cuya caracterización experimental muestra una resolución de más 8 bits para un ancho de banda analógico de 20 MHz. Concretamente, la resolución medida será mayor de 9 bits hasta una frecuencia de entrada de 2.9 GHz y mayor de 8 bits para una frecuencia de entrada de hasta 6.5 GHz, lo cual resulta suficiente para cubrir los requerimientos de la mayor parte de los actuales estándares de comunicaciones inalámbricas (GPS, GSM, GPRS, UMTS, Bluetooth, Wi-Fi, WiMAX). Sin embargo, los receptores basados en submuestreo presentan algunos importantes inconvenientes, como son adicionales fuentes de ruido (jitter y plegado de ruido térmico) y una dificultad añadida para implementarlo en escenarios multi-banda y no lineales. Acerca del plegado de ruido en la banda de interés, esta tesis propone el uso de una técnica basada en una arquitectura de reloj múltiple con el objetivo de aumentar la resolución y cubrir un número mayor de estándares para su test y certificación. Empleando una frecuencia de muestreo mayor para el caso del S&H, se conseguirá reducir este efecto, aumentando la resolución en aproximadamente 0.5-1 bit respecto al caso de sólo usar una fuente de reloj. Las expresiones teóricas de esta mejora son desarrolladas y presentadas en esta tesis, siendo posteriormente corroboradas de modo experimental. Por otra parte, esta tesis también propone novedosas técnicas para la aplicación de estos sistemas de submuestreo en entornos multi-banda y no lineales, los cuales presentan desafíos adicionales por el hecho de existir la posibilidad de solapamiento entre la señal de interés y los otros canales de comunicación, así como de solapamiento con sus armónicos. De este modo, esta tesis extiende el uso de los sistemas basados en submuestreo para este tipo de entornos, proponiendo técnicas para la elección de la frecuencia óptima de muestreo que evitan el solapamiento entre señales, a la vez que consiguen incrementar la resolución del receptor. Finalmente, se presentará la optimización en cuanto a características de ruido de un receptor concreto para aplicaciones de banda dual en entornos no lineales. Dicho receptor estará basado en las técnicas de reloj múltiple presentadas anteriormente y en una estructura de multi-filtro entre el S&H y el ADC. El sistema diseñado podrá emplearse para diversas aplicaciones a ambos lados de la cadena de comunicación, tal como en receptores de detección de espectro para radio cognitiva, o implementando el bucle de realimentación de un transmisor para la linealización de amplificadores de potencia. Por tanto, la presente tesis doctoral cuenta con tres contribuciones diferenciadas. La primera de ellas es la dedicada al diseño de un prototipo de recepción multi-estándar basado en submuestreo para aplicaciones de test y certificación. La segunda aportación es la dedicada a la optimización de las especificaciones de ruido a partir de las técnicas presentadas basadas en reloj múltiple. Por último, la tercera contribución principal es la relacionada con la extensión de este tipo de técnicas a sistemas multi-banda en entornos no lineales. Todas estas contribuciones han sido estudiadas teóricamente y experimentalmente validadas