# Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding

## TL;DR

This paper introduces a novel adaptive thresholding method for signal recovery from 1-bit noisy measurements, capable of handling arbitrary noise covariance, including colored noise, and recovering both fixed and time-varying signals.

## Contribution

It presents the first unified framework for 1-bit signal recovery in noisy environments using adaptive quadratic programming, accommodating arbitrary noise covariance structures.

## Key findings

- Effective recovery of signals from 1-bit noisy samples demonstrated
- Handles both white and colored noise with arbitrary covariance matrices
- Capable of recovering fixed and time-varying parameters

## Abstract

In this paper, we consider the problem of signal recovery from 1-bit noisy measurements. We present an efficient method to obtain an estimation of the signal of interest when the measurements are corrupted by white or colored noise. To the best of our knowledge, the proposed framework is the pioneer effort in the area of 1-bit sampling and signal recovery in providing a unified framework to deal with the presence of noise with an arbitrary covariance matrix including that of the colored noise. The proposed method is based on a constrained quadratic program (CQP) formulation utilizing an adaptive quantization thresholding approach, that further enables us to accurately recover the signal of interest from its 1-bit noisy measurements. In addition, due to the adaptive nature of the proposed method, it can recover both fixed and time-varying parameters from their quantized 1-bit samples.