##### Department of Mathematics,

University of California San Diego

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### Math 278C - Mathematics of Information, Data, and Signals Seminar

## Rongrong Wang

#### Michigan State University

## Sigma Delta quantization on images, manifolds, and graphs

##### Abstract:

In digital signal processing, quantization is the step of converting a signal's real-valued samples into a finite string of bits. As the first step in digital processing, it plays a crucial role in determining the information conversion rate and the reconstruction accuracy. Compared to non-adaptive quantizers, the adaptive ones are known to be more efficient in quantizing bandlimited signals, especially when the bit-budget is small (e.g.,1 bit) and noises are present. However, adaptive quantizers are currently only designed for 1D functions/signals. In this talk, I will discuss challenges in extending it to high dimensions and present our proposed solutions. Specifically, we design new adaptive quantization schemes to quantize images/videos as well as functions defined on 2D surface manifolds and general graphs, which are common objects in signal processing and machine learning. Mathematically, we start from the 1D Sigma-Delta quantization, extend them to high-dimensions and build suitable decoders. The discussed theory would be useful in natural image acquisition, medical imaging, 3D printing, and graph embedding.

### October 28, 2021

### 11:30 AM

Zoom link: https://msu.zoom.us/j/96421373881 (the passcode is the first prime number $>$ 100).

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