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The main purpose of this article is to establish the Runge-type approximation in $L^2(0,T;\widetilde{H}^s(\Omega))$ for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical…
The radiofrequency (RF) transmit field is severely inhomogeneous at ultrahigh field due to both RF penetration and RF coil design issues. This particularly impairs image quality for sequences that use inversion pulses such as magnetization…
The stepped-frequency (SF) waveform is an effective way to achieve high range resolution (HRR) in modern radars. In this paper, we determine some fundamental limits of SF waveforms on ambiguity, stability and accuracy of stable targets…
A stylized compressed sensing radar is proposed in which the time-frequency plane is discretized into an N by N grid. Assuming the number of targets K is small (i.e., K much less than N^2), then we can transmit a sufficiently "incoherent"…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
To relieve the interference caused by range-Doppler sidelobes in pulsed radars, we propose a new method to construct Doppler resilient complementary waveforms based on Golay codes. We design both the transmit pulse train and the receive…
In the last decade, metamaterials-based superlenses, with a resolution below Abbe's diffraction limit, have emerged. To obtain a rough estimate of the resolution of such superlenses, imaging of two subwavelength slits, separated by a…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…
In this paper we study the identification of a time-varying linear system from its response to a known input signal. More specifically, we consider systems whose response to the input signal is given by a weighted superposition of delayed…
Correctly detecting radar targets is usually challenged by clutter and waveform distortion. An additional difficulty stems from the relative proximity of several targets, the latter being perceived as a single target in the worst case, or…
In this paper, we employ the thoughts and methodologies of Shannon's information theory to solve the problem of the optimal radar parameter estimation. Based on a general radar system model, the \textit{a posteriori} probability density…
A large number of image super resolution algorithms based on the sparse coding are proposed, and some algorithms realize the multi-frame super resolution. In multi-frame super resolution based on the sparse coding, both accurate image…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
Integrated sensing and communication improves the design of systems by combining sensing and communication functions for increased efficiency, accuracy, and cost savings. The optimal integration requires understanding the trade-off between…
The newly emerging theory of compressed sensing (CS) enables restoring a sparse signal from inadequate number of linear projections. Based on compressed sensing theory, a new algorithm of high-resolution range profiling for…
We study super-resolution imaging theoretically using a distant n-mode interferometer in the microwave regime for passive remote sensing, used e.g., for satellites like the "soil moisture and ocean salinity (SMOS)" mission to observe the…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…