Research

My current research focuses on the following:

1. Adaptive Sensing/Sampling. In the classical setting, a measurement setup remains fixed throughout the process of data acquisition. In adaptive sensing, at every time step, the measurement setup is altered based on past measurements to overall maximize the information of interest. Some of the active areas of application of this concept appear in mine detection, see through the wall, SAR imaging, and target tracking.
2. Manifold Learning. Manifolds offer the capability to describe high dimensional data using a low dimensional representation. Dimensionality reduction of high-dimensional data that lies on a manifold allows visualization of the data, reduction in computational complexity of data processing, and the capability of intrinsic data processing. Areas of application include: medical diagnosis, target recognition, analysis of internet data, and sensor networks.
   
3. Sparse Representations for Signal Processing. We are interested in investigating data that is sparse according to some basis or dictionary. In other words, the data can be represented using only a small number of basis/dictionary elements. Image compression methods, which are based on vector quantization, demonstrate that an image can be represented in a sparse fashion through fixed bases, e.g., discrete cosine transform (DCT) and wavelets. Sparse reconstruction takes advantage of the signal sparsity in reproducing the signal from partial and/or noisy observations. Areas of application include: electromagnetic imaging, molecular imaging, and sensor/waveform selection.