DSP seminar, Wed May. 03 Time and location: 4:00-5:00 PM 2269 Beckman Institute

Title: Quantization and Erasures in Frame Representations


Speaker: Petros Boufounos


Abstract:

Frame representations, which correspond to overcomplete 
generalizations to basis expansions, are often used in signal 
processing to provide robustness to errors. After a brief background on 
frame representations, the use of projections is explored to compensate 
for errors in the representation coefficients, with focus on 
quantization and erasure errors. The projections are implemented by 
modifying the unaffected coefficients using an additive term, which is 
linear in the error. This low-complexity implementation only assumes 
linear reconstruction using a pre-determined synthesis frame, and makes 
no assumption on how the representation coefficients are generated.

In the context of quantization, a generalization of Sigma-Delta noise 
shaping to arbitrary frame representations is developed by 
reformulating noise shaping as a sequence of compensations for the 
quantization error using projections. The total error is quantified 
using both the additive noise model of quantization, and a 
deterministic upper bound based on the triangle inequality. It is thus 
shown that the average and the worst-case error is reduced compared to 
scalar quantization of the coefficients. Further applications of this 
principle to classical Sigma-Delta noise shaping for oversampled 
signals are also considered.

The projection principle is also used to provide robustness to 
erasures. Specifically, the case of a transmitter that is aware of the 
erasure occurrence is considered, which compensates for the erasure 
error by projecting it to the subsequent frame vectors. It is further 
demonstrated that the transmitter can be split to a 
transmitter/receiver combination that performs the same compensation, 
but in which only the receiver is aware of the erasure occurrence.
Furthermore, an algorithm to puncture dense representations in order to 
produce sparse approximate ones is introduced. In this algorithm the 
error due to the puncturing is also projected to the span of the 
remaining coefficients. The algorithm can be combined with quantization 
to produce quantized sparse representations approximating the original 
dense representation.


Biography: