arXiv subjects

Yonina C. Eldar

Publications and source records attributed to Yonina C. Eldar.

At least 361 records · Page 20Linked to original sources

arXiv2017

A General Framework for Low-Resolution Receivers for MIMO Channels

The capacity of a discrete-time multi-input multi-output (MIMO) Gaussian channel with output quantization is investigated for different receiver architectures. A general formulation of this problem is proposed in which the antenna outputs are processed by analog combiners while sign quantizers are used for analog-to-digital conversion. To exemplify this approach, four analog receiver architectures of varying generality and complexity are considered: (a) multiple antenna selection and sign quantization of the antenna outputs, (b) single antenna selection and multilevel quantization, (c) multiple antenna selection and multilevel quantization, and (d) linear combining of the antenna outputs and multilevel quantization. Achievable rates are studied as a function of the number of available sign quantizers and compared among different architectures. In particular, it is shown that architecture (a) is sufficient to attain the optimal high signal-to-noise ratio performance for a MIMO receiver in which the number of antennas is larger than the number of sign quantizers. Numerical evaluations of the average performance are presented for the case in which the channel gains are i.i.d. Gaussian.

cs.IT↗

arXiv2017

Low Rank Magnetic Resonance Fingerprinting

Purpose: Magnetic Resonance Fingerprinting (MRF) is a relatively new approach that provides quantitative MRI measures using randomized acquisition. Extraction of physical quantitative tissue parameters is performed off-line, without the need of patient presence, based on acquisition with varying parameters and a dictionary generated according to the Bloch equation simulations. MRF uses hundreds of radio frequency (RF) excitation pulses for acquisition, and therefore a high undersampling ratio in the sampling domain (k-space) is required for reasonable scanning time. This undersampling causes spatial artifacts that hamper the ability to accurately estimate the tissue's quantitative values. In this work, we introduce a new approach for quantitative MRI using MRF, called magnetic resonance Fingerprinting with LOw Rank (FLOR). Methods: We exploit the low rank property of the concatenated temporal imaging contrasts, on top of the fact that the MRF signal is sparsely represented in the generated dictionary domain. We present an iterative scheme that consists of a gradient step followed by a low rank projection using the singular value decomposition. Results: Experimental results consist of retrospective sampling, that allows comparison to a well defined reference, and prospective sampling that shows the performance of FLOR for a real-data sampling scenario. Both experiments demonstrate improved parameter accuracy compared to other compressed-sensing and low-rank based methods for MRF at 5% and 9% sampling ratios, for the retrospective and prospective experiments, respectively. Conclusions: We have shown through retrospective and prospective experiments that by exploiting the low rank nature of the MRF signal, FLOR recovers the MRF temporal undersampled images and provides more accurate parameter maps compared to previous iterative methods.

physics.med-ph↗

arXiv2017

PEAR: PEriodic And fixed Rank separation for fast fMRI

In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements. We decompose the fMRI signal into a component which a has fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI. Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R=8,16 (for simulated data) and R=6.66,10 (for real data). PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank+Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods.

physics.med-ph↗

arXiv2017

Sub-Nyquist SAR via Fourier Domain Range Doppler Processing

Conventional Synthetic Aperture Radar (SAR) systems are limited in their ability to satisfy the increasing requirement for improved spatial resolution and wider coverage. The demand for high resolution requires high sampling rates, while coverage is limited by the pulse repetition frequency. Consequently, sampling rate reduction is of high practical value in SAR imaging. In this paper, we introduce a new algorithm, equivalent to the well-known Range-Doppler method, to process SAR data using the Fourier series coefficients of the raw signals. We then demonstrate how to exploit the algorithm features to reduce sampling rate in both range and azimuth axes and process the signals at sub-Nyquist rates, by using compressed sensing (CS) tools. In particular, we demonstrate recovery of an image using only a portion of the received signal's bandwidth and also while dropping a large percentage of the transmitted pulses. The complementary pulses may be used to capture other scenes within the same coherent processing interval. In addition, we propose exploiting the ability to reconstruct the image from narrow bands in order to dynamically adapt the transmitted waveform energy to vacant spectral bands, paving the way to cognitive SAR. The proposed recovery algorithms form a new CS-SAR imaging method that can be applied to high-resolution SAR data acquired at sub-Nyquist rates in range and azimuth. The performance of our method is assessed using simulated and real data sets. Finally, our approach is implemented in hardware using a previously suggested Xampling radar prototype.

cs.IT↗

arXiv2017

Quantum State Tomography with a Single Observable

Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, and chemistry. These fundamental and applied aspects of quantum information rely on a crucial issue: the ability to characterize a quantum state from measurements, through a process called Quantum State Tomography (QST). However, QST requires a large number of measurements, each derived from a different physical observable corresponding to a different experimental setup. Unfortunately, changing the setup results in unwanted changes to the data, prolongs the measurement and impairs the assumptions that are always made about the stationarity of the noise. Here, we propose to overcome these drawbacks by performing QST with a single observable. A single observable can often be realized by a single setup, thus considerably reducing the experimental effort. In general, measurements of a single observable do not hold enough information to recover the quantum state. We overcome this lack of information by relying on concepts inspired by Compressed Sensing (CS), exploiting the fact that the sought state - in many applications of quantum information - is close to a pure state (and thus has low rank). Additionally, we increase the system dimension by adding an ancilla that couples to information evolving in the system, thereby providing more measurements, enabling the recovery of the original quantum state from a single-observable measurements. We demonstrate our approach on multi-photon states by recovering structured quantum states from a single observable, in a single experimental setup. We further show how this approach can be used to recover quantum states without number-resolving detectors.

quant-ph↗

arXiv2017

On the Uniqueness of FROG Methods

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultra-short laser pulse characterization in which the electromagnetic field is oscillating with ~10^15 Hz and phase information cannot be measured directly due to limitations of the electronic sensors. Phase retrieval is ill-posed in most cases as there are many different signals with the same Fourier transform magnitude. To overcome this fundamental ill-posedness, several measurement techniques are used in practice. One of the most popular methods for complete characterization of ultra-short laser pulses is the Frequency-Resolved Optical Gating (FROG). In FROG, the acquired data is the power spectrum of the product of the unknown pulse with its delayed replica. Therefore the measured signal is a quartic function of the unknown pulse. A generalized version of FROG, where the delayed replica is replaced by a second unknown pulse, is called blind FROG. In this case, the measured signal is quadratic with respect to both pulses. In this letter we introduce and formulate FROG-type techniques. We then show that almost all band-limited signals are determined uniquely, up to trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in addition we have access to the signals power spectrum.

cs.IT↗

arXiv2017

On the Minimax Capacity Loss under Sub-Nyquist Universal Sampling

This paper investigates the information rate loss in analog channels when the sampler is designed to operate independent of the instantaneous channel occupancy. Specifically, a multiband linear time-invariant Gaussian channel under universal sub-Nyquist sampling is considered. The entire channel bandwidth is divided into $n$ subbands of equal bandwidth. At each time only $k$ constant-gain subbands are active, where the instantaneous subband occupancy is not known at the receiver and the sampler. We study the information loss through a capacity loss metric, that is, the capacity gap caused by the lack of instantaneous subband occupancy information. We characterize the minimax capacity loss for the entire sub-Nyquist rate regime, provided that the number $n$ of subbands and the SNR are both large. The minimax limits depend almost solely on the band sparsity factor and the undersampling factor, modulo some residual terms that vanish as $n$ and SNR grow. Our results highlight the power of randomized sampling methods (i.e. the samplers that consist of random periodic modulation and low-pass filters), which are able to approach the minimax capacity loss with exponentially high probability.

cs.IT↗

arXiv2017

On Fienup Methods for Regularized Phase Retrieval

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex priors. In particular, we show that Fienup methods can be viewed as performing alternating minimization on a regularized nonconvex least-squares problem with respect to amplitude measurements. We then prove that under mild additional structural assumptions on the prior (semi-algebraicity), the sequence of signal estimates has a smooth convergent behaviour towards a critical point of the nonconvex regularized least-squares objective. Finally, we propose an extension to Fienup techniques, based on a projected gradient descent interpretation and acceleration using inertial terms. We demonstrate experimentally that this modification combined with an $\ell_1$ prior constitutes a competitive approach for sparse phase retrieval.

cs.IT↗

arXiv2017

Low Rank Phase Retrieval

We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both methods consist of a spectral initialization step followed by an iterative algorithm to maximize the observed data likelihood. We obtain sample complexity bounds for our proposed initialization approach to provide a good approximation of the true $\X$. When the rank is low enough, these bounds are significantly lower than what existing single vector phase retrieval algorithms need. Via extensive experiments, we show that the same is also true for the proposed complete algorithms.

cs.IT↗

arXiv2017

Online Dictionary Learning Aided Target Recognition In Cognitive GPR

Sparse decomposition of ground penetration radar (GPR) signals facilitates the use of compressed sensing techniques for faster data acquisition and enhanced feature extraction for target classification. In this paper, we investigate the application of an online dictionary learning (ODL) technique in the context of GPR to bring down the learning time as well as improve identification of abandoned anti-personnel landmines. Our experimental results using real data from an L-band GPR for PMN/PMA2, ERA and T72 mines show that ODL reduces learning time by 94\% and increases clutter detection by 10\% over the classical K-SVD algorithm. Moreover, the proposed methodology could be helpful in cognitive operation of the GPR where the system adapts the range sampling based on the learned dictionary.

cs.IT↗

arXiv2017

Performance of time delay estimation in a cognitive radar

A cognitive radar adapts the transmit waveform in response to changes in the radar and target environment. In this work, we analyze the recently proposed sub-Nyquist cognitive radar wherein the total transmit power in a multi-band cognitive waveform remains the same as its full-band conventional counterpart. For such a system, we derive lower bounds on the mean-squared-error (MSE) of a single-target time delay estimate. We formulate a procedure to select the optimal bands, and recommend distribution of the total power in different bands to enhance the accuracy of delay estimation. In particular, using Cramér-Rao bounds, we show that equi-width subbands in cognitive radar always have better delay estimation than the conventional radar. Further analysis using Ziv-Zakai bound reveals that cognitive radar performs well in low signal-to-noise (SNR) regions.

cs.IT↗

arXiv2016

FoCUS: Fourier-based Coded Ultrasound

Modern imaging systems typically use single-carrier short pulses for transducer excitation. Coded signals together with pulse compression are successfully used in radar and communication to increase the amount of transmitted energy. Previous research verified significant improvement in SNR and imaging depth for ultrasound imaging with coded signals. Since pulse compression needs to be applied at each transducer element, the implementation of coded excitation (CE) in array imaging is computationally complex. Applying pulse compression on the beamformer output reduces the computational load but also degrades both the axial and lateral point spread function (PSF) compromising image quality. In this work we present an approach for efficient implementation of pulse compression by integrating it into frequency domain beamforming. This method leads to significant reduction in the amount of computations without affecting axial resolution. The lateral resolution is dictated by the factor of savings in computational load. We verify the performance of our method on a Verasonics imaging system and compare the resulting images to time-domain processing. We show that up to 77 fold reduction in computational complexity can be achieved in a typical imaging setups. The efficient implementation makes CE a feasible approach in array imaging paving the way to enhanced SNR as well as improved imaging depth and frame-rate.

cs.IT↗

arXiv2016

Spectrum Sharing Radar: Coexistence via Xampling

This paper presents a spectrum sharing technology enabling interference-free operation of a surveillance radar and communication transmissions over a common spectrum. A cognitive radio receiver senses the spectrum using low sampling and processing rates. The radar is a cognitive system that employs a Xampling-based receiver and transmits in several narrow bands. Our main contribution is the alliance of two previous ideas, CRo and cognitive radar (CRr), and their adaptation to solve the spectrum sharing problem.

cs.IT↗

arXiv2016

WINDOW: Wideband Demodulator for Optical Waveforms

Optical communication systems, which operate at very high rates, are often limited by the sampling rate bottleneck. The optical wideband regime may exceed analog to digital converters (ADCs) front-end bandwidth. Multi-channel sampling approaches, such as multicoset or interleaved ADCs, have been proposed to sample the wideband signal using several channels. Each channel samples below the Nyquist rate such that the overall sampling rate is preserved. However, this scheme suffers from two practical limitations that make its implementation difficult. First, the inherent anti-aliasing filter of the samplers distorts the wideband signal. Second, it requires accurate time shifts on the order of the signal's Nyquist rate, which are challenging to maintain. In this work, we propose an alternative multi-channel sampling scheme, the wideband demodulator for optical waveforms (WINDOW), based on analog RF demodulation, where each channel aliases the spectrum using a periodic mixing function before integration and sampling. We show that intentionally using the inherent ADC filter to perform integration increases the signal to noise ratio (SNR). We demonstrate both theoretically and through numerical experiments that our system outperforms multicoset in terms of signal recovery and symbol estimation in the presence of both thermal and quantization noise but is slightly less robust to timing jitter.

cs.IT↗

arXiv2016

Sub-Nyquist Cyclostationary Detection for Cognitive Radio

Cognitive Radio requires efficient and reliable spectrum sensing of wideband signals. In order to cope with the sampling rate bottleneck, new sampling methods have been proposed that sample below the Nyquist rate. However, such techniques decrease the signal to noise ratio (SNR), deteriorating the performance of subsequent energy detection. Cyclostationary detection, which exploits the periodic property of communication signal statistics, absent in stationary noise, is a natural candidate for this setting. In this work, we consider cyclic spectrum recovery from sub-Nyquist samples, in order to achieve both efficiency and robustness to noise. To that end, we propose a structured compressed sensing algorithm, that extends orthogonal matching pursuit to account for the structure imposed by cyclostationarity. Next, we derive a lower bound on the sampling rate required for perfect cyclic spectrum recovery in the presence of stationary noise and show that it can be reconstructed from samples obtained below Nyquist, without any sparsity constraints on the signal. In particular, in non sparse settings, the cyclic spectrum can be recovered at $4/5$ of the Nyquist rate. If the signal of interest is sparse, then the sampling rate may be further reduced to $8/5$ of the Landau rate. Once the cyclic spectrum is recovered, we estimate the number of transmissions that compose the input signal, along with their carrier frequencies and bandwidths. Simulations show that cyclostationary detection outperforms energy detection in low SNRs in the sub-Nyquist regime. This was already known in the Nyquist regime, but is even more pronounced at sub-Nyquist sampling rates.

cs.IT↗

arXiv2016

Global testing against sparse alternatives in time-frequency analysis

In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram over-sampled by $O(\log N)$ is proven universally optimal in global testing for periodicities under a mild minimum separation condition.

math.ST↗

arXiv2016

SUMMeR: Sub-Nyquist MIMO Radar

Multiple input multiple output (MIMO) radar exhibits several advantages with respect to traditional radar array systems in terms of flexibility and performance. However, MIMO radar poses new challenges for both hardware design and digital processing. In particular, achieving high azimuth resolution requires a large number of transmit and receive antennas. In addition, the digital processing is performed on samples of the received signal, from each transmitter to each receiver, at its Nyquist rate, which can be prohibitively large when high resolution is needed. Overcoming the rate bottleneck, sub-Nyquist sampling methods have been proposed that break the link between radar signal bandwidth and sampling rate. In this work, we extend these methods to MIMO configurations and propose a sub-Nyquist MIMO radar (SUMMeR) system that performs both time and spatial compression. We present a range-azimuth-Doppler recovery algorithm from sub-Nyquist samples obtained from a reduced number of transmitters and receivers, that exploits the sparsity of the recovered targets' parameters. This allows us to achieve reduction in the number of deployed antennas and the number of samples per receiver, without degrading the time and spatial resolutions. Simulations illustrate the detection performance of SUMMeR for different compression levels and shows that both time and spatial resolution are preserved, with respect to classic Nyquist MIMO configurations. We also examine the impact of design parameters, such as antennas' locations and carrier frequencies, on the detection performance, and provide guidelines for their choice.

cs.IT↗

arXiv2016

The Distortion Rate Function of Cyclostationary Gaussian Processes

A general expression for the distortion rate function (DRF) of cyclostationary Gaussian processes in terms of their spectral properties is derived. This expression can be seen as the result of orthogonalization over the different components in the polyphase decomposition of the process. We use this expression to derive, in a closed form, the DRF of several cyclostationary processes arising in practice. We first consider the DRF of a combined sampling and source coding problem. It is known that the optimal coding strategy for this problem involves source coding applied to a signal with the same structure as one resulting from pulse amplitude modulation (PAM). Since a PAM-modulated signal is cyclostationary, our DRF expression can be used to solve for the minimal distortion in the combined sampling and source coding problem. We also analyze in more detail the DRF of a source with the same structure as a PAM-modulated signal, and show that it is obtained by reverse waterfilling over an expression that depends on the energy of the pulse and the baseband process modulated to obtain the PAM signal. This result is then used to study the information content of a PAM-modulated signal as a function of its symbol time relative to the bandwidth of the underlying baseband process. In addition, we also study the DRF of sources with an amplitude-modulation structure, and show that the DRF of a narrow-band Gaussian stationary process modulated by either a deterministic or a random phase sine-wave equals the DRF of the baseband process.

cs.IT↗