DSP Seminar
Thursday, April 5, 3-4pm
2269 Beckman Institute

Title: Optimal Super-Resolution without Input Assumptions

Speaker: Ha T. Nguyen, Graduate Student, ECE



Abstract:

We study the problem of super-resolution (SR) that synthesizes a high
resolution signal from multiple low resolution signals. The low resolution
signals are sampled versions of the same continuous-domain signal with
different fractional delays. The system to provide SR consists of a
synthesis filter bank that upsamples, filters the low resolution signals in
each channel and sums them up to obtain high resolution signals. 
Instead of relying on assumptions about input signals (such as band- 
limitedness), we develop a system that minimizes the worst approximation error 
over all input signals of finite energy. This is equivalent to minimizing the
$\mathcal{H}_{\infty}$ norm of a hybrid induced error system. We show that
this induced error system is equivalent to a discrete-domain system with IIR
analysis filters. To design the SR synthesis filter banks, we use powerful
tools in control theory including model-matching and linear matrix
inequality that have implementations available in MATLAB. Numerical
experiments show our approach to be superior to existing techniques,
especially in the presence of high frequencies.