[Paper Review] Off-grid Variational Bayesian Inference of Line Spectral Estimation from One-bit Samples.

Jiang Zhu, Qi Zhang+1 more|arXiv (Cornell University)|Nov 14, 2018

Blind Source Separation Techniques48 references4 citations

TL;DR

This paper proposes VALSE-EP, a variational Bayesian inference method for off-grid line spectral estimation from one-bit quantized samples. By decomposing the quantized model into a minimum mean square error (MMSE) module and a standard linear model, the algorithm iteratively refines frequency estimates via expectation propagation, demonstrating superior performance in challenging one-bit scenarios and extending naturally to multiple measurement vectors.

ABSTRACT

In this paper, the line spectral estimation (LSE) problem is studied from one-bit quantized samples where variational line spectral estimation (VALSE) combined expectation propagation (EP) VALSE-EP method is proposed. Since the original measurements are heavily quantized, performing the off-grid frequency estimation is very challenging. Referring to the expectation propagation (EP) principle, this quantized model is decomposed as two modules, one is the componentwise minimum mean square error (MMSE) module, the other is the standard linear model where the variational line spectrum estimation (VALSE) algorithm can be performed. The VALSE-EP algorithm iterates between the two modules in a turbo manner. In addition, this algorithm can be easily extended to solve the LSE with the multiple measurement vectors (MMVs). Finally, numerical results demonstrate the effectiveness of the proposed VALSE-EP method.

Motivation & Objective

• To address the challenge of off-grid frequency estimation when measurements are severely quantized to one bit.
• To develop a robust inference framework that maintains accuracy despite extreme quantization loss.
• To extend the method to handle multiple measurement vectors (MMVs) for improved spectral estimation.
• To leverage variational Bayesian inference and expectation propagation for efficient, iterative frequency estimation.

Proposed method

• The VALSE-EP algorithm decomposes the one-bit quantized model into two modules: a componentwise MMSE module and a standard linear model.
• It employs expectation propagation (EP) to iteratively update posterior approximations in a turbo-like fashion between the two modules.
• The variational line spectral estimation (VALSE) algorithm is applied within the linear model module to estimate the line spectrum.
• The method alternates between updating the MMSE approximation and refining the spectral estimates via variational inference.
• The framework is naturally extendable to multiple measurement vectors (MMVs) by generalizing the linear model component.
• The algorithm ensures convergence through iterative message passing between the two model components.

Experimental results

Research questions

• RQ1 How can accurate off-grid frequency estimation be achieved from one-bit quantized samples?
• RQ2 Can variational Bayesian inference effectively handle the non-Gaussian, highly quantized likelihood in one-bit sampling?
• RQ3 How does the VALSE-EP method compare to existing approaches in terms of spectral resolution and robustness under extreme quantization?
• RQ4 Can the proposed framework be extended to multiple measurement vectors (MMVs) with minimal modification?

Key findings

• The VALSE-EP method achieves high-resolution line spectral estimation even under one-bit quantization, outperforming conventional methods in challenging conditions.
• The iterative EP-based refinement between the MMSE and linear model modules improves estimation accuracy and convergence stability.
• The method demonstrates robust performance in off-grid scenarios where traditional grid-based methods fail.
• The framework is naturally extendable to multiple measurement vectors (MMVs), enabling efficient joint spectral estimation.