Sparse Reconstruction of Compressive Sensing Magnetic Resonance Imagery using a Cross Domain Stochastic Fully Connected Conditional Random Field Framework

Prostate cancer is a major health care concern in our society. Early detection of prostate cancer is crucial in the successful treatment of the disease. Many current methods used in detecting prostate cancer can either be inconsistent or invasive and discomforting to the patient. Magnetic resonance imaging (MRI) has demonstrated its ability as a non-invasive and non-ionizing medical imaging modality with a lengthy acquisition time that can be used for the early diagnosis of cancer. Speeding up the MRI acquisition process can greatly increase the number of early detections for prostate cancer diagnosis. Compressive sensing has exhibited the ability to reduce the imaging time for MRI by sampling a sparse yet sufficient set of measurements. Compressive sensing strategies are usually accompanied by strong reconstruction algorithms. This work presents a comprehensive framework for a cross-domain stochastically fully connected conditional random field (CD-SFCRF) reconstruction approach to facilitate compressive sensing MRI. This approach takes into account original k-space measurements made by the MRI machine with neighborhood and spatial consistencies of the image in the spatial domain. This approach facilitates the difference in domain between MRI measurements made in the k-space, and the reconstruction results in spatial domain. An adaptive extension of the CD-SFCRF approach that takes into account regions of interest in the image and changes the CD-SFCRF neighborhood connectivity based on importance is presented and tested as well. Finally, a compensated CD-SFCRF approach that takes into account MRI machine imaging apparatus properties to correct for degradations and aberrations from the image acquisition process is presented and tested. Clinical MRI data were collected from twenty patients with ground truth data examined and con firmed by an expert radiologist with multiple years of prostate cancer diagnosis experience. Compressive sensing simulations were performed and the reconstruction results show the CD-SFCRF and extension frameworks having noticeable improvements over state of the art methods. Tissue structure and image details are well preserved while sparse sampling artifacts were reduced and eliminated. Future work on this framework include extending the current work in multiple ways. Extensions including integration into computer aided diagnosis applications as well as improving on the compressive sensing strategy

Simultaneous Multispectral Imaging: Using Multiview Computational Compressive Sensing

Multispectral imaging is traditionally performed using a combination of an imaging device with a filter bank such as a filter wheel or a form of tunable filter, or a combination of many imaging devices with various spectral beam splitting optics. The complexity and size of these devices seem to be the limiting factor of their adoption and use in various fields that could potentially benefit from this imaging modality. With the advent of nanophotonics, there has been a surge in single camera, snapshot, multispectral imaging exploiting the capabilities of nanotechnology to devise pixel-based spectral filters. This new form of sensing, which can be classified as compressive sensing, has its limitations. One example is the laborious process of fabricating the filter bank and installing it into a detector since the detector fabrication process is completely removed from the filter fabrication process. The work presented here will describe an optical design that would enable a single-camera, simultaneous multispectral imaging via multiview computational compressive sensing. A number of points-of-view (POVs) of the field-of-view (FOV) of the camera are generated and directed through an assortment of spectral pre-filters en route to the camera. The image of each of the POVs is then captured on a different spatial location on the detector. With the spectral response of the detector pixels well characterized, spatial and spectral compressive sensing is performed as the images are recorded. Various computational techniques are used in this work which would: register the images captured from multiple views resulting in even more sparsely sensed images; perform spatial interpolation of the sparsely sampled spectral images; implement hyper-focusing of the images from all POVs captured as some defocusing will happen as the result of the discrepancy in the optical paths in each view; execute numerical dimensionality reduction analysis to extract information from the multispectral images. The spectral imaging capabilities of the device are tested with a collection of fluorescent microspheres. The spectral sensing capability of the device is examined by measuring the fluorescent spectra of adulterated edible oils and demonstrating the ability of the imaging system to differentiate between various types of oil as well as various levels of contamination. Lastly, the system is used to scrutinize samples of black ink from different pen manufacturers, and is able to discriminate between the different inks

Anomaly detection & object classification using multi-spectral LiDAR and sonar

In this thesis, we present the theory of high-dimensional signal approximation of multifrequency signals. We also present both linear and non-linear compressive sensing (CS) algorithms that generate encoded representations of time-correlated single photon counting (TCSPC) light detection and ranging (LiDAR) data, side-scan sonar (SSS) and synthetic aperture sonar (SAS). The main contributions of this thesis are summarised as follows: 1. Research is carried out studying full-waveform (FW) LiDARs, in particular, the TCSPC data, capture, storage and processing. 2. FW-LiDARs are capable of capturing large quantities of photon-counting data in real-time. However, the real-time processing of the raw LiDAR waveforms hasn’t been widely exploited. This thesis answers some of the fundamental questions: • can semantic information be extracted and encoded from raw multi-spectral FW-LiDAR signals? • can these encoded representations then be used for object segmentation and classification? 3. Research is carried out into signal approximation and compressive sensing techniques, its limitations and the application domains. 4. Research is also carried out in 3D point cloud processing, combining geometric features with material spectra (spectral-depth representation), for object segmentation and classification. 5. Extensive experiments have been carried out with publicly available datasets, e.g. the Washington RGB Image and Depth (RGB-D) dataset [108], YaleB face dataset1 [110], real-world multi-frequency aerial laser scans (ALS)2 and an underwater multifrequency (16 wavelengths) TCSPC dataset collected using custom-build targets especially for this thesis. 6. The multi-spectral measurements were made underwater on targets with different shapes and materials. A novel spectral-depth representation is presented with strong discrimination characteristics on target signatures. Several custom-made and realistically scaled exemplars with known and unknown targets have been investigated using a multi-spectral single photon counting LiDAR system. 7. In this work, we also present a new approach to peak modelling and classification for waveform enabled LiDAR systems. Not all existing approaches perform peak modelling and classification simultaneously in real-time. This was tested on both simulated waveform enabled LiDAR data and real ALS data2 . This PhD also led to an industrial secondment at Carbomap, Edinburgh, where some of the waveform modelling algorithms were implemented in C++ and CUDA for Nvidia TX1 boards for real-time performance. 1http://vision.ucsd.edu/~leekc/ExtYaleDatabase/ 2This dataset was captured in collaboration with Carbomap Ltd. Edinburgh, UK. The data was collected during one of the trials in Austria using commercial-off-the-shelf (COTS) sensors

Bayesian methods for inverse problems with point clouds : applications to single-photon lidar

Single-photon light detection and ranging (lidar) has emerged as a prime candidate technology for depth imaging through challenging environments. This modality relies on constructing, for each pixel, a histogram of time delays between emitted light pulses and detected photon arrivals. The problem of estimating the number of imaged surfaces, their reflectivity and position becomes very challenging in the low-photon regime (which equates to short acquisition times) or relatively high background levels (i.e., strong ambient illumination). In a general setting, a variable number of surfaces can be observed per imaged pixel. The majority of existing methods assume exactly one surface per pixel, simplifying the reconstruction problem so that standard image processing techniques can be easily applied. However, this assumption hinders practical three-dimensional (3D) imaging applications, being restricted to controlled indoor scenarios. Moreover, other existing methods that relax this assumption achieve worse reconstructions, suffering from long execution times and large memory requirements. This thesis presents novel approaches to 3D reconstruction from single-photon lidar data, which are capable of identifying multiple surfaces in each pixel. The resulting algorithms obtain new state-of-the-art reconstructions without strong assumptions about the sensed scene. The models proposed here differ from standard image processing tools, being designed to capture correlations of manifold-like structures. Until now, a major limitation has been the significant amount of time required for the analysis of the recorded data. By combining statistical models with highly scalable computational tools from the computer graphics community, we demonstrate 3D reconstruction of complex outdoor scenes with processing times of the order of 20 ms, where the lidar data was acquired in broad daylight from distances up to 320 m. This has enabled robust, real-time target reconstruction of complex moving scenes, paving the way for single-photon lidar at video rates for practical 3D imaging applications

NON-LINEAR REGULARIZATION FOR IMAGING THROUGH TURBID MEDIA

Ph.DDOCTOR OF PHILOSOPH

Compressive sensing for signal ensembles

Compressive sensing (CS) is a new approach to simultaneous sensing and compression that enables a potentially large reduction in the sampling and computation costs for acquisition of signals having a sparse or compressible representation in some basis. The CS literature has focused almost exclusively on problems involving single signals in one or two dimensions. However, many important applications involve distributed networks or arrays of sensors. In other applications, the signal is inherently multidimensional and sensed progressively along a subset of its dimensions; examples include hyperspectral imaging and video acquisition. Initial work proposed joint sparsity models for signal ensembles that exploit both intra- and inter-signal correlation structures. Joint sparsity models enable a reduction in the total number of compressive measurements required by CS through the use of specially tailored recovery algorithms. This thesis reviews several different models for sparsity and compressibility of signal ensembles and multidimensional signals and proposes practical CS measurement schemes for these settings. For joint sparsity models, we evaluate the minimum number of measurements required under a recovery algorithm with combinatorial complexity. We also propose a framework for CS that uses a union-of-subspaces signal model. This framework leverages the structure present in certain sparse signals and can exploit both intra- and inter-signal correlations in signal ensembles. We formulate signal recovery algorithms that employ these new models to enable a reduction in the number of measurements required. Additionally, we propose the use of Kronecker product matrices as sparsity or compressibility bases for signal ensembles and multidimensional signals to jointly model all types of correlation present in the signal when each type of correlation can be expressed using sparsity. We compare the performance of standard global measurement ensembles, which act on all of the signal samples; partitioned measurements, which act on a partition of the signal with a given measurement depending only on a piece of the signal; and Kronecker product measurements, which can be implemented in distributed measurement settings. The Kronecker product formulation in the sparsity and measurement settings enables the derivation of analytical bounds for transform coding compression of signal ensembles and multidimensional signals. We also provide new theoretical results for performance of CS recovery when Kronecker product matrices are used, which in turn motivates new design criteria for distributed CS measurement schemes

Compressed Sensing Beyond the IID and Static Domains: Theory, Algorithms and Applications

Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions using few measurements, where i.i.d measurements are at disposal. However real world scenarios typically exhibit non i.i.d and dynamic structures and are confined by physical constraints, preventing applicability of the theoretical guarantees of compressed sensing and limiting its applications. In this thesis we develop new theory, algorithms and applications for non i.i.d and dynamic compressed sensing by considering such constraints. In the first part of this thesis we derive new optimal sampling-complexity tradeoffs for two commonly used processes used to model dependent temporal structures: the autoregressive processes and self-exciting generalized linear models. Our theoretical results successfully recovered the temporal dependencies in neural activities, financial data and traffic data. Next, we develop a new framework for studying temporal dynamics by introducing compressible state-space models, which simultaneously utilize spatial and temporal sparsity. We develop a fast algorithm for optimal inference on such models and prove its optimal recovery guarantees. Our algorithm shows significant improvement in detecting sparse events in biological applications such as spindle detection and calcium deconvolution. Finally, we develop a sparse Poisson image reconstruction technique and the first compressive two-photon microscope which uses lines of excitation across the sample at multiple angles. We recovered diffraction-limited images from relatively few incoherently multiplexed measurements, at a rate of 1.5 billion voxels per second

Channel Estimation in Multi-user Massive MIMO Systems by Expectation Propagation based Algorithms

Massive multiple input multiple output (MIMO) technology uses large antenna arrays with tens or hundreds of antennas at the base station (BS) to achieve high spectral efficiency, high diversity, and high capacity. These benefits, however, rely on obtaining accurate channel state information (CSI) at the receiver for both uplink and downlink channels. Traditionally, pilot sequences are transmitted and used at the receiver to estimate the CSI. Since the length of the pilot sequences scale with the number of transmit antennas, for massive MIMO systems downlink channel estimation requires long pilot sequences resulting in reduced spectral efficiency and the so-called pilot contamination due to sharing of the pilots in adjacent cells. In this dissertation we first review the problem of channel estimation in massive MIMO systems. Next, we study the problem of semi-blind channel estimation in the uplink in the case of spatially correlated time-varying channels. The proposed method uses the transmitted data symbols as virtual pilots to enhance channel estimation. An expectation propagation (EP) algorithm is developed to iteratively approximate the joint a posterior distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. The distribution is then used for direct estimation of the channel matrix and detection of the data symbols. A modified version of Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize our algorithm. Simulation results demonstrate that channel estimation error and the symbol error rate of the proposed algorithm improve with the increase in the number of BS antennas or the number of data symbols in the transmitted frame. Moreover, the proposed algorithms can mitigate the effects of pilot contamination as well as time-variations of the channel. Next, we study the problem of downlink channel estimation in multi-user massive MIMO systems. Our approach is based on Bayesian compressive sensing in which the clustered sparse structure of the channel in the angular domain is exploited to reduce the pilot overhead. To capture the clustered structure, we employ a conditionally independent identically distributed Bernoulli-Gaussian prior on the sparse vector representing the channel, and a Markov prior on its support vector. An EP algorithm is developed to approximate the intractable joint distribution on the sparse vector and its support with a distribution from an exponential family. This distribution is then used for direct estimation of the channel. The EP algorithm requires the model parameters which are unknown. We estimate these parameters using the expectation maximization (EM) algorithm. Simulation results show that the proposed combination of EM and EP referred to as EM-EP algorithm outperforms several recently-proposed algorithms in the literature