I am interested in research problems at the interface between mathematics, sciences, and engineering. I work on the development of mathematical methodologies and computational tools to extract information from complex data, specially when the data are scarce. Mathematically, this includes compressed sensing tools, new optimization approaches, and data analysis. My applied research ranges from the use of optimization methods in imaging, in particular in the development of data-driven algorithms, to other inverse problems that can benefit from the same or similar algorithms.
Interests
- Compressive sensing
- Mathematical optimization
- Direct and inverse scattering in random media
Latest
- Quantitative Phase and Absorption Contrast Imaging
- Fast Signal Recovery from Quadratic Measurements
- Sparse signal recovery from correlation measurements using the noise collector
- Three-dimensional imaging from single-element holographic data
- Imaging with highly incomplete and corrupted data
- Robust multifrequency imaging with MUSIC
- A Closed-Form Formula for the RBF-Based Approximation of the Laplace–Beltrami Operator
- Quantitative subsurface imaging in strongly scattering media
- Multifrequency interferometric imaging with intensity-only measurements
- Array imaging of localized objects in homogeneous and heterogeneous media
- Coherent imaging without phases
- Optimized Finite Difference Formulas for Accurate High Frequency Components
- Radial basis function interpolation in the limit of increasingly flat basis functions
- Synthetic aperture imaging of direction- and frequency-dependent reflectivities
- Illumination strategies for intensity-only imaging
- Laurent expansion of the inverse of perturbed, singular matrices
- Laurent series based RBF-FD method to avoid ill-conditioning
- Imaging strong localized Scatterers with Sparsity promoting optimization
- Recovering fluorophore location and orientation from lifetimes
- Robust depth selectivity in mesoscopic scattering regimes using angle-resolved measurements
- Robust imaging of localized scatterers using the singular value decomposition and ℓ1 minimization
- A differential equations approach to l 1-minimization with applications to array imaging
- Combining diffuse optical tomography and spectroscopy to detect and characterize lesions in two-layered tissues
- Gaussian RBF-FD weights and its corresponding local truncation errors
- Gaussian RBF-FD weights and its corresponding local truncation errors
- Optimal variable shape parameter for multiquadric based RBF-FD method
- Shape reconstruction of cardiac ischemia from non-contact intracardiac recordings: A model study
- Source location from fluorescence lifetime in disordered media
- Array imaging using intensity-only measurements
- Diffusion of polarized light
- Optimal constant shape parameter for multiquadric based RBF-FD method
- Application of the RBF meshless method to the solution of the radiative transport equation
- Passive imaging with cross correlations in a discrete random medium
- RBF-FD formulas and convergence properties
- Structural level set inversion for microwave breast screening
- An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium
- Crack reconstruction using a level-set strategy
- Detecting and imaging dielectric objects from real data: A shape-based approach
- Fluorescence lifetime imaging from time resolved measurements using a shape-based approach
- Microwave imaging for early breast cancer detection using a shape-based strategy
- A level set evolution strategy in microwave imaging for early breast cancer detection
- Introduction to image reconstruction
- Polarization-based optical imaging
- Reservoir characterization using stochastic initializations and the level set method
- Imaging low sensitivity regions in petroleum reservoirs using topological perturbations and level sets
- On the stability of surface shape reconstruction using microwave algorithm for 3-D breast tumor based on the adjoint-fields scheme
- Reconstructing a thin absorbing obstacle in a half-space of tissue
- Reconstruction of transmembrane currents using support vector machines and its application to endocardial mapping: A model study
- Detection of small tumors in microwave medical imaging using level sets and music
- Radiative transport theory for optical molecular imaging
- History matching problem in reservoir engineering using the propagation-backpropagation method
- Light transport in two-layer tissues
- Light transport in two-layer tissues.
- Backscattering of beams by forward-peaked scattering media
- Beam propagation in sharply peaked forward scattering media
- Backscattering of circularly polarized pulses
- Beam propagation in multiple scattering media
- Radiative transfer computations for optical beams
- Backscattering of circularly polarized pulses
- Chebyshev spectral methods for radiative transfer
- Depolarization and blurring of optical images by biological tissue
- Influence of the relative index on the depolarization of multiply scattered waves
- Influence of the relative refractive index on the depolarization of multiply scattered waves
- Optical polarization imaging in biological tissue
- Spatiotemporal structures in undoped photoexcited semiconductor superlattices
- Theoretical and numerical analysis of polarization for time-dependent radiative transfer equations
- Bifurcation behavior of a superlattice model
- Dynamics of electric field domain walls in semiconductor superlattices
- Polarization effects of seismic waves on the basis of radiative transport theory
- Current self-oscillations, spikes, and crossover between charge monopole and dipole waves in semiconductor superlattices
- Drift model of resonant tunneling in superlattices including a time delay simulating electron scattering mechanisms
- Current-voltage characteristic and stability in resonant-tunneling n-dopedsemiconductor superlattices
- Microscopic model for sequential tunneling in semiconductor multiple quantum wells
- Periodic generation and propagation of traveling fronts in dc voltage biased semiconductor superlattices
- Spikes in the current self-oscillations of doped GaAs/AlAs superlattices
- Dynamics of electric-field domains and Chaos in semiconductor superlattices
- Self-oscillations of domains in doped GaAs-AlAs superlattices
- Self-oscillations of the current in doped semiconductor superlattices