APPLICATIONS IN
SIGNAL
DENOISING
In a joint work with Andrew Bruce (MathSoft, Seattle) and Sylvain Sardy
(EPFL, Lausanne), we developed numerical methods for
signal denoising using wavelet basis. We reformulated
the problem as an optimization problem (in fact, a convex quadratic
program with special structures) and we applied a block-coordinate
relaxation (Gauss-Seidel) method as well as a primal-dual interior-point
method to its solution. Two applications of this signal denoising problem
are shown below. The images were generated by Sylvain and are taken from
the technical reports detailing our work, available soon from
my homepage.
- 1. Electronic surveillance:
The application concerns passive detection and finger printing
of incoming radar signatures from an electronic surveillance platform. The observed signal is 2048 samples from a chirped RF source at 3 decibels with jamming interference. The top image shows the
observed signal and the bottom image shows the signal after it is
denoised using wavelet Basis Pursuit.
- 2. Denoising a contaminated function:
The top graph shows the original heavisine function.
The bottom left graph shows the function after contamination.
The bottom right graph shows the contaminated function after it is
denoised using wavelet Robust Basis Pursuit.