Speaker: dr. P. (Palina) Salanevich
Title: "Noise-shaping quantization with Gabor frames”
Abstract:
In digital signal processing, all operations are performed on digitalized signals, even though these signals are usually analogous in nature. This makes quantization, that is, analog-to-digital signal conversion, an essential problem in the field of digital signal processing. The distributed noise shaping approach, introduced by Chou and Gunturk, refers to a quantization methodology in which a redundant representation of a signal with respect to a frame is used to arrange the quantization error to lie as close as possible to the kernel of a dual frame synthesis matrix. In this talk, we will focus on this quantization approach in the special case of Gabor frames, which provide time-frequency signal representation and appear naturally in many audio and image processing applications. More specifically, we will show that for Gabor frames with a properly chosen window, distributed beta-encoding coupled with reconstruction via beta-duals leads to nearly optimal quantization error. Furthermore, we will discuss the dependence of the quantization error on the Gabor window structure and the condensation order in the distributed beta-encoding.
The talk is based on a joint work with Sinan Gunturk and Goetz Pfander.