Searcharxiv⌕ Search

arXiv subjects

Lianlin Li

Publications and source records attributed to Lianlin Li.

35 records · Page 2Linked to original sources
arXiv2014

Far-field Imaging beyond the Diffraction Limit Using a Single Radar

Far-field imaging beyond the diffraction limit is a long sought-after goal in various imaging applications, which requires usually an array of antennas or mechanical scanning. Here, we present an alternative and novel concept for this challenging problem: a single radar system consisting of a spatial-temporal resonant aperture antenna (referred to as the slavery antenna) and a broadband horn antenna (termed the master antenna). We theoretically demonstrate that such resonant aperture antenna is responsible for converting parts of the evanescent waves into propagating waves, and delivering them to the far-field. We also demonstrate that there are three basic requirements on the proposed subwavelength imaging strategy: the strong spatial-temporal dispersive aperture, the near-field coupling, and the temporal (or broadband) illumination. Such imaging concept of a single radar provides unique ability to produce real-time data when an object is illuminated by broadband electromagnetic waves, which lifts up the harsh requirements such as near-field scanning, mechanical scanning or antenna arrays remarkably. We expect that this imaging methodology will make breakthroughs in super-resolution imaging in the microwave, terahertz, optical, and ultrasound regimes.

physics.optics↗
arXiv2014

Theory of the far-field imaging beyond the Rayleigh limit based on the super-resonant lens

Essentially, the idea of improving the resolution of a given imaging system is to enhance its information capacity represented usually by the temporal-bandwidth (or, spatial-spectrum) product. This letter introduces the concept of super-resonant lens, and demonstrates theoretically that the information capacity of a far-field imaging system can be efficiently driven up when three basic requirements are satisfied: the super-resonance, the near-field coupling between imaged objects and the used super-resonant lens, and the broadband illumination, which leads to the subwavelength image of imaged objects from far-field measurements. Furthermore, a single-view imaging scheme is proposed and examined for the far-field imaging beyond the diffraction limit. This new approach will be a breakthrough in nanolithography, detection, sensing or sub-wavelength imaging in the near future.

physics.optics↗
arXiv2014

Far-field subwavelength imaging from a single broadband antenna in combined with strongly disordered medium

The far-field subwavlength imaging is a challenging issue. In this letter we demonstrate numerically that the far-field subwavelength imaging of weakly scattering objects can be obtained by processing the data acquired by a single antenna, which benefits from the use of the strongly disordered medium. A mathematical model has been proposed for solving such problem based on the idea of sparse reconstruction. Moreover, this study leads to an important conclusion that the strongly disordered medium can serves as an efficient apparatus for the single-antenna compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

physics.optics↗
arXiv2014

Subwavelength imaging of sparse broadband sources surrounded by an open disordered medium from a single antenna

In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea of sparse reconstruction. We show that the strongly disordered medium can serves as an efficient apparatus for compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

physics.optics↗
arXiv2013

Beat the Rayleigh limit: OAM based super-resolution diffraction tomography

This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). It is well accepted that the orbital angular momentum (OAM) provides additional electromagnetic degrees of freedom. This concept has been widely applied in science and technology. In this letter we revisit the DT problem extended with OAM, demonstrate theoretically and numerically that there is no physical limits on imaging resolution in principle by the OAM-DT. This super-resolution OAM-DT imaging paradigm, has no requirement for evanescent fields, subtle focusing lens, complicated post-processing, etc., thus provides a new approach to realize the wavefield imaging of universal objects with sub-wavelength resolution.

physics.optics↗
arXiv2012

Note on RIP-based Co-sparse Analysis

Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More recently, its counterpart, i.e., the sparse analysis model, has also attracted researcher's attentions where many practical signals which are sparse in the truly redundant dictionary are concerned. This short paper presents important complement to the results in existing literatures for treating sparse analysis model. Firstly, we give the natural generalization of well-known restricted isometry property (RIP) to deal with sparse analysis model, where the truly arbitrary incoherent dictionary is considered. Secondly, we studied the theoretical guarantee for the accurate recovery of signal which is sparse in general redundant dictionaries through solving l1-norm sparsity-promoted optimization problem. This work shows not only that compressed sensing is viable in the context of sparse analysis, but also that accurate recovery is possible via solving l1-minimization problem.

cs.IT↗
arXiv2011

The Statistical Coherence-based Theory of Robust Recovery of Sparsest Overcomplete Representation

The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This problem can be stated in the following, i.e., to seek for the sparse coefficient vector of the given noisy observation over a redundant dictionary such that, where is the corrupted error. Elad et al. made the worst-case result, which shows the condition of stable recovery of sparest overcomplete representation over is where . Although it's of easy operation for any given matrix, this result can't provide us realistic guide in many cases. On the other hand, most of popular analysis on the sparse reconstruction relies heavily on the so-called RIP (Restricted Isometric Property) for matrices developed by Candes et al., which is usually very difficult or impossible to be justified for a given measurement matrix. In this article, we introduced a simple and efficient way of determining the ability of given D used to recover the sparse signal based on the statistical analysis of coherence coefficients, where is the coherence coefficients between any two different columns of given measurement matrix . The key mechanism behind proposed paradigm is the analysis of statistical distribution (the mean and covariance) of . We proved that if the resulting mean of are zero, and their covariance are as small as possible, one can faithfully recover approximately sparse signals from a minimal number of noisy measurements with overwhelming probability. The resulting theory is not only suitable for almost all models - e.g. Gaussian, frequency measurements-discussed in the literature of compressed sampling, but also provides a framework for new measurement strategies as well.

cs.IT↗
arXiv2009

An Iteratively Reweighted Algorithm for Sparse Reconstruction of Subsurface Flow Properties from Nonlinear Dynamic Data

In this paper, we present a practical algorithm based on sparsity regularization to effectively solve nonlinear dynamic inverse problems that are encountered in subsurface model calibration. We use an iteratively reweighted algorithm that is widely used to solve linear inverse problems with sparsity constraint known as compressed sensing to estimate permeability fields from nonlinear dynamic flow data.

math.NA↗
arXiv2009

Compressive sensing by white random convolution

A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the coherence (denoted by mu) between the signal representation and the Fourier basis. In particular, an n-dimensional signal which is S-sparse in such a basis can be recovered with a probability exceeding 1-delta from any fixed m~O(mu^2*S*log(n/delta)^(3/2)) output samples of the random convolution.

math.OC↗
arXiv2009

Novel Algorithm for Sparse Solutions to Linear Inverse Problems with Multiple Measurements

In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly sparse recovery is obviously superior to applying standard sparse reconstruction methods to each channel individually. Moreover several efforts have been made to improve the NESTA-based MMV algorithm, in particular, (1) the NESTA-based MMV algorithm for partially known support to greatly improve the convergence rate, (2) the detection of partial (or all) locations of unknown jointly sparse signals by using so-called MUSIC algorithm; (3) the iterative NESTA-based algorithm by combing hard thresholding technique to decrease the numbers of measurements. It has been shown that by using proposed approach one can recover the unknown sparse matrix X with () Spark A -sparsity from () Spark A measurements, predicted in Ref. [1], where the measurement matrix denoted by A satisfies the so-called restricted isometry property (RIP). Under a very mild condition on the sparsity of X and characteristics of the A, the iterative hard threshold (IHT)-based MMV method has been shown to be also a very good candidate.

cs.IT↗
arXiv2009

Compressive Diffraction Tomography for Weakly Scattering

An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution reconstruction from highly sparse data for the weakly scatters has been investigated in this paper. To realize the compressive data measurement, in particular, to obtain the super-resolution reconstruction with highly sparse data, the compressive system which is realized by surrounding the probed obstacles by the random media has been proposed and empirically studied. Several interesting conclusions have been drawn: (a) if the desired resolution is within the range from to, the K-sparse N-unknowns imaging can be obtained exactly bymeasurements, which is comparable to the required number of measurement by the Gaussian random matrix in the literatures of compressive sensing. (b) With incorporating the random media which is used to enforce the multi-path effect of wave propagation, the resulting measurement matrix is incoherence with wavelet matrix, in other words, when the probed obstacles are sparse with the framework of wavelet, the required number of measurements for successful reconstruction is similar as above. (c) If the expected resolution is lower than, the required number of measurements of proposed compressive system is almost identical to the case of free space. (d) There is also a requirement to make the tradeoff between the imaging resolutions and the number of measurements. In addition, by the introduction of complex Gaussian variable the kind of fast sparse Bayesian algorithm has been slightly modified to deal with the complex-valued optimization with sparse constraints.

cs.CE↗
arXiv2009

A Novel Algorithm for Compressive Sensing: Iteratively Reweighed Operator Algorithm (IROA)

Compressive sensing claims that the sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. One of issues ensuring the successful compressive sensing is to deal with the sparsity-constraint optimization. Up to now, many excellent theories, algorithms and software have been developed, for example, the so-called greedy algorithm ant its variants, the sparse Bayesian algorithm, the convex optimization methods, and so on. The formulations for them consist of two terms, in which one is and the other is (, mostly, p=1 is adopted due to good characteristic of the convex function) (NOTE: without the loss of generality, itself is assumed to be sparse). It is noted that all of them specify the sparsity constraint by the second term. Different from them, the developed formulation in this paper consists of two terms where one is with () and the other is . For each iteration the measurement matrix (linear operator) is reweighed by determined by which is obtained in the previous iteration, so the proposed method is called the iteratively reweighed operator algorithm (IROA). Moreover, in order to save the computation time, another reweighed operation has been carried out; in particular, the columns of corresponding to small have been excluded out. Theoretical analysis and numerical simulations have shown that the proposed method overcomes the published algorithms.

cs.IT↗
arXiv2008

The Design of Compressive Sensing Filter

In this paper, the design of universal compressive sensing filter based on normal filters including the lowpass, highpass, bandpass, and bandstop filters with different cutoff frequencies (or bandwidth) has been developed to enable signal acquisition with sub-Nyquist sampling. Moreover, to control flexibly the size and the coherence of the compressive sensing filter, as an example, the microstrip filter based on defected ground structure (DGS) has been employed to realize the compressive sensing filter. Of course, the compressive sensing filter also can be constructed along the identical idea by many other structures, for example, the man-made electromagnetic materials, the plasma with different electron density, and so on. By the proposed architecture, the n-dimensional signals of S-sparse in arbitrary orthogonal frame can be exactly reconstructed with measurements on the order of Slog(n) with overwhelming probability, which is consistent with the bonds estimated by theoretical analysis.

cs.CE↗
arXiv2008

The Design of Sparse Antenna Array

The aim of antenna array synthesis is to achieve a desired radiation pattern with the minimum number of antenna elements. In this paper the antenna synthesis problem is studied from a totally new perspective. One of the key principles of compressive sensing is that the signal to be sensed should be sparse or compressible. This coincides with the requirement of minimum number of element in the antenna array synthesis problem. In this paper the antenna element of the array can be efficiently reduced via compressive sensing, which shows a great improvement to the existing antenna synthesis method. Moreover, the desired radiation pattern can be achieved in a very computation time which is even shorter than the existing method. Numerical examples are presented to show the high efficiency of the proposed method.

cs.IT↗
arXiv2008

Theoretical Analysis of Compressive Sensing via Random Filter

In this paper, the theoretical analysis of compressive sensing via random filter, firstly outlined by J. Romberg [compressive sensing by random convolution, submitted to SIAM Journal on Imaging Science on July 9, 2008], has been refined or generalized to the design of general random filter used for compressive sensing. This universal CS measurement consists of two parts: one is from the convolution of unknown signal with a random waveform followed by random time-domain subsampling; the other is from the directly time-domain subsampling of the unknown signal. It has been shown that the proposed approach is a universally efficient data acquisition strategy, which means that the n-dimensional signal which is S sparse in any sparse representation can be exactly recovered from Slogn measurements with overwhelming probability.

cs.IT↗