Research Page

Data Science: Signal Processing on Graphs or Graph Signal Processing

This is a new area of research that builds on our previous work on Algebraic Signal Processing. It develops data analytics for unstructured data, i.e., data that does not fit well in a table. The data is indexed by the nodes of a graph, rather than by the time instants of a speech or audio signal or the pixels of an image, or voxels of a video. The data is called a graph signal. The underlying graph is arbitrary; it can be undirected, directed, or mixed. The graph G=(V,E) collects the nodes in the set V. The edges in the set E connect nodes of the graph. The edges represent dependencies among the data indexed by the nodes. Undirected edges usually capture a dual dependency, like the color of a pixel depends on the color of both neighbors and vice-versa, the color of my neigboring pixel also depends on the color of the original pixel. A directed edge represents a causal relation like the samples of a time series, the sample at time n depends on the sample at time n-1.

Signal Processing

To be added. Follow links below to Cognitive Networks, Sensor Networks, Time Reversal Imaging, Time Reversal Infrastructure Health Monitoring, and AFM: MOSAIC for additional details.

Cognitive Networks    Sensor Networks    Time Reversal Imaging    Time Reversal Infrastructure Health Monitoring    AFM: MOSAIC

Image and Video Processing

To be added. Follow links below for additional information.

Statistical Theory of Shape  Image & Video Representation

Bioimaging

To be added.

Magnetic Resonance Imaging

Communications

To be added.

Radar, Sonar, Array Processing     Detection Estimation
Non-Linear & Kalman Bucy Filtering High Density Recording

Algebraic Signal Processing and Transforms

There are two main projects: SPIRAL and DSP on Graphs that build on the previous project SMART.

SPIRAL is an interdisciplinary project involving a large multi University interdisciplinary team of experts in signal processing, compilers, computer architecture, and artificial intelligence. SPIRAL develops fast implementations of digital signal processing (DSP) algorithms, for example, C or Fortran code, that is optimized for the specific platform of interest. The code that SPIRAL generates automatically is highly competitive. In fact it can be better than the code provided by vendor hand-tuned libraries (follow the link below to SPIRAL and see some of the papers and presentations on SPIRAL).

Major support to SPIRAL has been provided by the DARPA ACMP OPAL Initiative through an ARMY research grant and by an NSF ITR medium size grant.

DSP on GRAPHS develops an Digital Signal Processing for signals that are indexed by general graphs.

SMART develops an Algebraic Approach to Digital Signal Processing. While SPIRAL uses the existing fast algorithms developed by researchers through their ingenuity and intuition and then automatically develops implementations for signal processing algorithms, SMART researches ways to automatically "invent" these fast algorithms, in this goal, it is like a "meta"-SPIRAL. Follow the link below for additional information and papers on SMART.

SMART has been supported by two grants from NSF, CISE Division, CCR Program.

SPIRAL     DSP on GRAPHS     SMART