"Distributed noise shaping quantization with Gabor frames"Salanevich, PalinaIn 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. |
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