# Romberg

### From Wikimization

# JUSTIN ROMBERG

Justin Romberg received the BS (1997), MS (1999), and PhD (2003) degrees in Electrical and Computer Engineering from Rice University. Romberg co-authored many publications with Prof. Richard Baraniuk at Rice, and was a Texas Instruments Distinguished Graduate Fellow. Romberg spent Fall 2003 as visitor at Laboratoire Jacques-Louis Lions at Paris VI, and Fall 2004 as visiting Fellow at UCLA's Institute for Pure and Applied Mathematics. He was a Postdoctoral Scholar in Applied and Computational Mathematics at Caltech from 2003 until 2006. He joined Georgia Institute of Technology in 2006 as Assistant Professor in the School of Electrical and Computer Engineering.

Justin Romberg won the Office of Naval Research Young Investigator Award in 2008
for his proposal “Compressive Sampling for Next-Generation Signal Acquisition".
Dr. Romberg's research focuses on mathematics of data acquisition.
He is interested in how randomness increases efficiency in data acquisition, in particular, reducing both cost and computational complexity of high-resolution sensing systems.
This work will influence the design of next-generation analog-to-digital converters, radar imaging platforms, and Magnetic Resonance Imaging (MRI) systems.

## Compressed Sensing: A Tutorial

## Course Notes for ECE 6250, Advanced Topics in Digital Signal Processing, Fall 2007, Georgia Tech

- sampling theory
- changing the sampling rate
- sneak preview of filter banks
- random processes and LTI systems
- oversampling and quantization
- noise shaping and quantization
- introduction to vector spaces
- inner products and orthobases
- Parseval and JPEG
- Gram-Schmidt
- norm Approximation and IRLS
- Shannon wavelets
- Shannon wavelets cont. and Haar Wavelets
- multiresolution analysis
- wavelet approximation and design
- the discrete wavelet transform and 2D wavelets
- wavelet applications: denoising and compression
- wavelets and time-frequency tilings
- introduction to least-squares signal processing
- the SVD and least-squares
- the pseudo inverse and stable reconstruction
- Tikhonov regularization and total least-squares
- weighted least-squares and best linear unbiased estimators
- recursive least-squares and the Kalman filter
- Pisarenko and MUSIC
- the Karhunen-Loeve Transform and Principal Components Analysis
- bandlimited reconstruction
- alternating projections and POCS