## Research Interests

- Apply Artificial Intelligence techniques to improve business management.
- Machine Learning for signal/image classification, detection and estimation.
- Signal Processing for Communications and Bio-engineering.
- High Performance Computing.
- Image and Video Processing: compression, filtering, denoising and enhancement.
- Robust and Nonlinear Signal Processing.

#### Compressive Sensing Signal Reconstruction by Weighted Median Regression Estimates

In this work, we propose a simple and robust algorithm for compressive sensing (CS) signal reconstruction based on the weighted
median (WM) operator. The proposed approach addresses the reconstruction problem by solving a l0-regularized least absolute deviation
(l0-LAD) regression problem with a tunable regularization parameter, being suitable for applications where the underlying contamination
follows a statistical model with heavier-than-Gaussian tails. The solution to this regularized LAD regression problem is efficiently
computed, under a coordinate descent framework, by an iterative algorithm that comprises two stages. In the first stage, an estimation
of the sparse signal is found by recasting the reconstruction problem as a parameter location estimation for each entry in the sparse
vector leading to the minimization of a sum of weighted absolute deviations. The solution to this one-dimensional minimization problem
turns out to be the WM operator acting on a shifted-and-scaled version of the measurement samples with weights taken from the entries
in the measurement matrix. The resultant estimated value is then passed to a second stage that identifies whether the corresponding
entry is relevant or not. This stage is achieved by a hard threshold operator with adaptable thresholding parameter that is suitably
tuned as the algorithm progresses. This two-stage operation, WM operator followed by a hard threshold operator, adds the desired
robustness to the estimation of the sparse signal and, at the same time, ensures the sparsity of the solution. Extensive simulations
demonstrate the reconstruction capability of the proposed approach under different noise models. We compare the performance of the
proposed approach to those yielded by state-of-the-art CS reconstruction algorithms showing that our approach achieves a better
performance for different noise distributions. In particular, as the distribution tails become heavier the performance gain
achieved by the proposed approach increases significantly.

Google Citations
#### Ultra-Wideband Compressed Sensing: Channel Estimation

In this work, ultra-wideband (UWB) channel estimation based on the theory of compressive sensing (CS) is developed. The proposed
approach relies on the fact that transmitting an ultra-short pulse through a multipath UWB channel leads to a received UWB signal
that can be approximated by a linear combination of a few atoms from a pre-defined dictionary, yielding thus a sparse representation
of the received UWB signal. The key in the proposed approach is in the design of a dictionary of parameterized waveforms (atoms) that
closely matches the information-carrying pulseshape leading thus to higher energy compaction and sparse representation, and, therefore
higher probability for CS reconstruction. Two approaches for UWB channel estimation are developed under a data-aided framework.
In the first approach, the CS reconstruction capabilities are exploited to recover the composite pulse-multipath channel from a reduced
set of random projections. This reconstructed signal is subsequently used as a referent template in a correlator-based detector.
In the second approach, from a set of random projections of the received pilot signal, the Matching Pursuit algorithm is used to
identify the strongest atoms in the projected signal that, in turn, are related to the strongest propagation paths that composite
the multipath UWB channel. A Rake like receiver uses those atoms as templates for the bank of correlators in the detection stage.
The bit error rate performances of the proposed approaches are analyzed and compared to that of traditional correlator-based
detector. Extensive simulations show that for different propagation scenarios and UWB communication channels, detectors based on
CS channel estimation outperform traditional correlator using just 1/3 of the sampling rate leading thus to a reduced use of
analog-to-digital resources in the channel estimation stage.

Google Citations