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We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et al, J. Comput. Phys., 385 (2019) 13-32], where the…
We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random motion; in addition sensors measurements…
Clipping is one of the simplest peak-to-average power ratio (PAPR) reduction schemes for orthogonal frequency division multiplexing (OFDM). Deliberately clipping the transmission signal degrades system performance, and clipping mitigation…
In this paper, we present solvable, convex formulations of $H_2$-optimal state estimation and state-feedback control problems for a general class of linear Partial Differential Equations (PDEs) with one spatial dimension. These convex…
We analyze the information efficiency of a deep-space optical communication link with background noise employing the pulse position modulation (PPM) format and a direct-detection receiver based on Geiger-mode photon counting. The…
The performance of linear receive beamforming in continuous-aperture array (CAPA)-based uplink communications is analyzed. Three continuous beamforming techniques are proposed under the criteria of maximum-ratio combining (MRC),…
Magnetic resonance imaging (MRI) based electrical properties tomography (EPT) is the quantification of the conductivity and permittivity of different tissues. These electrical properties can be obtained through different reconstruction…
We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their measurements to a cluster head (CH). CHs optimally fuse the received signals and…
This paper provides analytical performance of the low-complexity family of affine projection algorithms on the estimation of multipath Rayleigh fading channels in the presence of carrier frequency offsets (CFO) and random channel…
Nonlinear distortion in power amplifiers (PA) can significantly degrade performance of orthogonal frequency division multiplexed (OFDM) communication systems. This paper presents a joint maximum-likelihood channel frequency response and…
We apply the iterative Expectation-Maximization algorithm (EM) to estimate the power spectrum of the CMB from multifrequency microwave maps. In addition, we are also able to provide a reconstruction of the CMB map. By assuming that the…
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
In the linear minimum mean square error (LMMSE) estimation for orthogonal frequency division multiplexing (OFDM) systems, the problem about the determination of the algorithm's parameters, especially those related with channel frequency…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…
Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential…
In the recent context of Software Defined Optical Network, the fast and accurate Quality of Transmission (QoT) estimation of the transmission link is essential. Gaussian Noise models are shown to yield a fast estimation of the average QoT…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…