On High-Resolution Adaptive Sampling of Deterministic Signals

TL;DR

This paper establishes a theoretical connection between high-resolution adaptive sampling and high-rate quantization, proposing a new practical nonuniform sampling method for deterministic signals that improves over existing techniques.

Contribution

It introduces a fundamental paradigm linking sampling and quantization, provides a theoretical analysis of high-resolution nonuniform sampling, and offers a practical sampling approach for 1D signals.

Findings

The optimal sampling structure depends on the signal-gradient energy density.

The proposed method outperforms optimized tree-structured sampling in experiments.

A new practical approach enables reconstruction using only sampling points and extrema.

Abstract

In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal high-resolution sampling, counterparts of well-known results for high-rate quantization. Our results reveal that the optimal high-resolution sampling structure is determined by the density of the signal-gradient energy, just as the probability-density-function defines the optimal high-rate quantization form. This paper has three main contributions: the first is establishing a fundamental paradigm bridging the topics of sampling and quantization. The second is a theoretical analysis of nonuniform sampling relevant to the emerging field of high-resolution signal processing. The third is a new practical approach to nonuniform sampling of one-dimensional signals that enables reconstruction based only on the sampling time-points and the signal extrema locations and values. Experiments for signal sampling and coding showed that our method outperforms an optimized tree-structured sampling technique.