Results 1  10
of
19
Exact joint sparse frequency recovery via optimization methods,” Available online at arXiv
, 2014
"... Frequency recovery/estimation from samples of superimposed sinusoidal signals is a classical problem in statistical signal processing. Its research has been recently advanced by atomic norm techniques which deal with continuousvalued frequencies and completely eliminate basis mismatches of existing ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Frequency recovery/estimation from samples of superimposed sinusoidal signals is a classical problem in statistical signal processing. Its research has been recently advanced by atomic norm techniques which deal with continuousvalued frequencies and completely eliminate basis mismatches of existing compressed sensing methods. This work investigates the frequency recovery problem in the presence of multiple measurement vectors (MMVs) which share the same frequency components, termed as joint sparse frequency recovery and arising naturally from array processing applications. `0 and `1normlike formulations, referred to as atomic `0 norm and the atomic norm, are proposed to recover the frequencies and cast as (nonconvex) rank minimization and (convex) semidefinite programming, respectively. Their guarantees for exact recovery are theoretically analyzed which extend existing results with a single measurement vector (SMV) to the MMV case and meanwhile generalize the existing joint sparse compressed sensing framework to the continuous dictionary setting. In particular, given a set of N regularly spaced samples per measurement vector it is shown that the frequencies can be exactly recovered via solving a convex optimization problem once they are separate by at least (approximately) 4N. Under the same frequency separation condition, a random subset of N regularly spaced samples of size O (K logK logN) per measurement vector is sufficient to guarantee exact recovery of the K frequencies and missing samples with high probability via similar convex optimization. Extensive numerical simulations are provided to validate our analysis and demonstrate the effectiveness of the proposed method.
Convex Optimization Approaches for Blind Sensor Calibration using Sparsity
, 2013
"... We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse s ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. The first proposed approach is an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. Demonstrating that this approach is successful for a sufficient number of input signals except in cases where the phase shifts among the unknown gains varies significantly, a second approach is proposed that makes use of quadratic basis pursuit optimization to calibrate for constant amplitude gains with maximum variance in the phases. An alternative form of this approach is also formulated to reduce the complexity and memory requirements and provide scalability with respect to the number of input signals. Finally a third approach is formulated which combines the first two approaches for calibration of systems with any variation in the gains. The performance of the proposed algorithms are investigated extensively through numerical simulations, which demonstrate that simultaneous signal recovery and calibration is possible when sufficiently many (unknown, but sparse) calibrating signals are provided.
Blind Sensor Calibration in Sparse Recovery Using Convex Optimization
, 2013
"... Abstract—We investigate a compressive sensing system in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on a few unknown (but sparse) signals. We extend our earlier study on real positive gains to two ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We investigate a compressive sensing system in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on a few unknown (but sparse) signals. We extend our earlier study on real positive gains to two generalized cases (signed realvalued gains; complexvalued gains), and show that the recovery of unknown gains together with the sparse signals is possible in a wide variety of scenarios. The simultaneous recovery of the gains and the sparse signals is formulated as a convex optimization problem which can be solved easily using offtheshelf algorithms. Numerical simulations demonstrate that the proposed approach is effective provided that sufficiently many (unknown, but sparse) calibrating signals are provided, especially when the sign or phase of the unknown gains are not completely random. I.
Joint Sparse Recovery Method for Compressed Sensing with Structured Dictionary Mismatches
"... ar ..."
(Show Context)
STABLE SIGNAL RECOVERY IN COMPRESSED SENSING WITH A STRUCTURED MATRIX PERTURBATION
"... The sparse signal recovery in standard compressed sensing (CS) requires that the sensing matrix is exactly known. The CS problem subject to perturbation in the sensing matrix is often encountered in practice and has attracted interest of researches. Unlike existing robust signal recoveries with the ..."
Abstract
 Add to MetaCart
(Show Context)
The sparse signal recovery in standard compressed sensing (CS) requires that the sensing matrix is exactly known. The CS problem subject to perturbation in the sensing matrix is often encountered in practice and has attracted interest of researches. Unlike existing robust signal recoveries with the recovery error growing linearly with the perturbation level, this paper analyzes the CS problem subject to a structured perturbation to provide conditions for stable signal recovery under measurement noise. Under mild conditions on the perturbed sensing matrix, similar to that for the standard CS, it is shown that a sparse signal can be stably recovered by 1 minimization. A remarkable result is that the recovery is exact and independent of the perturbation if there is no measurement noise and the signal is sufficiently sparse. In the presence of noise, largest entries (in magnitude) of a compressible signal can be stably recovered. The result is demonstrated by a simulation example. Index Terms — Compressed sensing, matrix perturbation, stable signal recovery, robust signal recovery
www.mdpi.com/journal/remotesensing Article Sparse Frequency Diverse MIMO Radar Imaging for OffGrid Target Based on Adaptive Iterative MAP
, 2013
"... Abstract: The frequency diverse multipleinputmultipleoutput (FDMIMO) radar synthesizes a wideband waveform by transmitting and receiving multiple frequency signals simultaneously. For FDMIMO radar imaging, conventional imaging methods based on Matched Filter (MF) cannot enjoy good imaging perfo ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract: The frequency diverse multipleinputmultipleoutput (FDMIMO) radar synthesizes a wideband waveform by transmitting and receiving multiple frequency signals simultaneously. For FDMIMO radar imaging, conventional imaging methods based on Matched Filter (MF) cannot enjoy good imaging performance owing to the few and incomplete wavenumberdomain coverage. Higher resolution and better imaging performance can be obtained by exploiting the sparsity of the target. However, good sparse recovery performance is based on the assumption that the scatterers of the target are positioned at the prediscretized grid locations; otherwise, the performance would significantly degrade. Here, we propose a novel approach of sparse adaptive calibration recovery via iterative maximum a posteriori (SACRiMAP) for the general offgrid FDMIMO radar imaging. SACRiMAP contains three loop stages: sparse recovery, offgrid errors calibration and parameter update. The convergence and the initialization of the method are also discussed. Numerical simulations are carried out to verify the effectiveness of the proposed method.
A CONJUGATE GRADIENT ALGORITHM FOR BLIND SENSOR CALIBRATION IN SPARSE RECOVERY
"... This work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sensing. It aims to estimate the unknown complex gains on each sensor, given a set of measurements of some unknown training signals. We assume that the unknown training signals are all spa ..."
Abstract
 Add to MetaCart
(Show Context)
This work studies the problem of blind sensor calibration (BSC) in linear inverse problems, such as compressive sensing. It aims to estimate the unknown complex gains on each sensor, given a set of measurements of some unknown training signals. We assume that the unknown training signals are all sparse. Instead of solving the problem by using convex optimization, we propose a cost function on a suitable manifold, namely, the set of complex diagonal matrices with determinant one. Such a construction can enhance numerical stabilities of the proposed algorithm. By exploring a global parameterization of the manifold, we tackle the BSC problem with a conjugate gradient method. Several numerical experiments are provided to oppose our approach to the solutions given by convex optimization and to demonstrate its performance. Index Terms — Blind sensor calibration, compressive sensing, conjugate gradient algorithm. 1.
SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 LowComplexity Multiclass Encryption by Compressed Sensing Part I: Definition and Main Properties
"... Abstract—The idea that compressed sensing may be used to encrypt information from unauthorized receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we use the simplicity of this encoding to ..."
Abstract
 Add to MetaCart
Abstract—The idea that compressed sensing may be used to encrypt information from unauthorized receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we use the simplicity of this encoding to define a general, lightweight encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, enabled to decode the original signal with provably different quality levels. The security properties of this scheme are thoroughly analyzed: first, the multiclass encryption features are theoretically investigated by deriving a lower bound on the quality degradation suffered by lowerclass receivers. Then, we perform a statistical analysis of the ciphertexts (measurements) to show that, although not perfectly secure, compressed sensing grants some level of encryption that comes at almostzero cost and thus may benefit resourcelimited applications. In addition to this, we report some example applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal reconstructions. Index Terms—Compressed sensing, encryption, physicallayer security, secure communications I.
SPARSE MRI FOR MOTION CORRECTION
"... MR image sparsity/compressibility has been widely exploited for imaging acceleration with the development of compressed sensing. A sparsitybased approach to rigidbody motion correction is presented for the first time in this paper. A motion is sought after such that the compensated MR image is ma ..."
Abstract
 Add to MetaCart
(Show Context)
MR image sparsity/compressibility has been widely exploited for imaging acceleration with the development of compressed sensing. A sparsitybased approach to rigidbody motion correction is presented for the first time in this paper. A motion is sought after such that the compensated MR image is maximally sparse/compressible among the infinite candidates. Iterative algorithms are proposed that jointly estimate the motion and the image content. The proposed method has a lot of merits, such as no need of additional data and loose requirement for the sampling sequence. Promising results are presented to demonstrate its performance. 1.
SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
"... Abstract—The mathematical theory of superresolution developed recently by Candès and FernandesGranda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of regularly spaced timespace samples. This theory w ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—The mathematical theory of superresolution developed recently by Candès and FernandesGranda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of regularly spaced timespace samples. This theory was then extended to the cases with partial/compressive samples and/or multiple measurement vectors via atomic norm minimization (ANM), known as offgrid/continuous compressed sensing. However, a major problem of existing atomic norm methods is that the frequencies can be recovered only if they are sufficiently separated, prohibiting commonly known high resolution. In this paper, a novel nonconvex optimization method is proposed which guarantees exact recovery under no resolution limit and hence achieves high resolution. A locally convergent iterative algorithm is implemented to solve the nonconvex problem. The algorithm iteratively carries out ANM with a sound reweighting strategy which enhances sparsity and resolution, and is termed as reweighted atomicnorm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the performance of the proposed method with application to direction of arrival (DOA) estimation. Index Terms—Continuous compressed sensing (CCS), DOA estimation, frequency estimation, gridless sparse method, high resolution, reweighted atomic norm minimization (RAM). I.