92 research outputs found
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Optimization in MRI Experiment Design and Image Reconstruction
Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality with numerous applications due to its flexible contrast and high resolution. Recent improvements in computation power have enabled optimizations which were previously out of reach. This has led to improvements in image reconstruction and experiment design.
Compressed sensing (CS) allows for images to be reconstructed using less data than is normally required leading to faster image acquisitions. In this thesis, CS is applied to experiments tracking individual cells in time lapse MRI. The faster image acquisition with CS reduces blurring from cell motion, improving the Contrast-to-Noise ratio (CNR) of moving cells and allows faster cells to be detected.
Pi Echo Planar Imaging (PEPI) is an MRI pulse sequence that allows high resolution images to be acquired quickly with relatively low gradient duty cycle. Low field applications benefit significantly from low gradient duty cycle as it reduces concomitant magnetic field artifacts, so PEPI is an attractive option for affordable low field scanners. However, there are challenges in implementing PEPI, due to its high requirement on the flip angle of the Ï RF pulses. Deviation of the flip angle causes coherence pathway artifacts restricting PEPI to small samples in the homogeneous region of the RF coil and preventing 2D slice selective experiment. In this thesis, the coherence pathway artifacts are addressed using an optimized phase cycling scheme, reducing the flip angle sensitivity, and enabling a slice selective PEPI sequence
Very High Resolution Tomographic SAR Inversion for Urban Infrastructure Monitoring â A Sparse and Nonlinear Tour
The topic of this thesis is very high resolution (VHR) tomographic SAR inversion for urban infrastructure monitoring. To this end, SAR tomography and differential SAR tomography are demonstrated using TerraSAR-X spotlight data for providing 3-D and 4-D (spatial-temporal) maps of an entire high rise city area including layover separation and estimation of deformation of the buildings. A compressive sensing based estimator (SL1MMER) tailored to VHR SAR data is developed for tomographic SAR inversion by exploiting the sparsity of the signal. A systematic performance assessment of the algorithm is performed regarding elevation estimation accuracy, super-resolution and robustness. A generalized time warp method is proposed which enables differential SAR tomography to estimate multi-component nonlinear motion. All developed methods are validated with both simulated and extensive processing of large volumes of real data from TerraSAR-X
Beyond the spatio-temporal limits of atmospheric radars: inverse problem techniques and MIMO systems
The Earthâs upper atmosphere (UA) is a highly dynamic region dominated by atmospheric waves and stratified turbulence covering a wide range of spatio-temporal scales. A comprehensive study of the UA requires measurements over a broad range of frequencies and spatial wavelengths, which are prohibitively costly. To improve the understanding of the UA, an investment in efficient and large observational infrastructures is required. This work investigates remote sensing techniques based on MIMO and inverse problems techniques to improve the capabilities of current atmospheric radars
Image Restoration Methods for Retinal Images: Denoising and Interpolation
Retinal imaging provides an opportunity to detect pathological and natural age-related
physiological changes in the interior of the eye. Diagnosis of retinal abnormality requires an image that is sharp, clear and free of noise and artifacts. However, to prevent tissue damage, retinal imaging instruments use low illumination radiation, hence, the signal-to-noise ratio (SNR) is reduced which means the total noise power is increased. Furthermore, noise is inherent in some imaging techniques. For example, in Optical Coherence Tomography (OCT) speckle noise is produced due to the coherence between the unwanted backscattered light. Improving OCT image quality by reducing speckle noise increases the accuracy of analyses and hence the diagnostic sensitivity. However, the challenge is to preserve image features while reducing speckle noise. There is a clear trade-off between image feature preservation and speckle noise reduction in OCT.
Averaging multiple OCT images taken from a unique position provides a high SNR
image, but it drastically increases the scanning time. In this thesis, we develop a multi-frame image denoising method for Spectral Domain OCT (SD-OCT) images extracted from a very close locations of a SD-OCT volume. The proposed denoising method was tested using two dictionaries: nonlinear (NL) and KSVD-based adaptive dictionary. The NL dictionary was constructed by adding phases, polynomial, exponential and boxcar functions to the conventional Discrete Cosine Transform (DCT) dictionary. The proposed denoising method denoises nearby frames of SD-OCT volume using a sparse representation method and combines them by selecting median intensity pixels from the denoised nearby frames. The result showed that both dictionaries reduced the speckle noise from the OCT images; however, the adaptive dictionary showed slightly better results at the cost of a higher computational complexity. The NL dictionary was also used for fundus and OCT image reconstruction. The performance of the NL dictionary was always better than that of other analytical-based dictionaries, such as DCT and Haar.
The adaptive dictionary involves a lengthy dictionary learning process, and therefore
cannot be used in real situations. We dealt this problem by utilizing a low-rank approximation. In this approach SD-OCT frames were divided into a group of noisy matrices that consist of non-local similar patches. A noise-free patch matrix was obtained from a noisy patch matrix utilizing a low-rank approximation. The noise-free patches from nearby frames were averaged to enhance the denoising. The denoised image obtained from the proposed approach was better than those obtained by several state-of-the-art methods. The proposed approach was extended to jointly denoise and interpolate SD-OCT image. The results show that joint denoising and interpolation method outperforms several existing state-of-the-art denoising methods plus bicubic interpolation.4 month
Advanced Techniques for Ground Penetrating Radar Imaging
Ground penetrating radar (GPR) has become one of the key technologies in subsurface sensing and, in general, in non-destructive testing (NDT), since it is able to detect both metallic and nonmetallic targets. GPR for NDT has been successfully introduced in a wide range of sectors, such as mining and geology, glaciology, civil engineering and civil works, archaeology, and security and defense. In recent decades, improvements in georeferencing and positioning systems have enabled the introduction of synthetic aperture radar (SAR) techniques in GPR systems, yielding GPRâSAR systems capable of providing high-resolution microwave images. In parallel, the radiofrequency front-end of GPR systems has been optimized in terms of compactness (e.g., smaller Tx/Rx antennas) and cost. These advances, combined with improvements in autonomous platforms, such as unmanned terrestrial and aerial vehicles, have fostered new fields of application for GPR, where fast and reliable detection capabilities are demanded. In addition, processing techniques have been improved, taking advantage of the research conducted in related fields like inverse scattering and imaging. As a result, novel and robust algorithms have been developed for clutter reduction, automatic target recognition, and efficient processing of large sets of measurements to enable real-time imaging, among others. This Special Issue provides an overview of the state of the art in GPR imaging, focusing on the latest advances from both hardware and software perspectives
Sensor Signal and Information Processing II
In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing
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