Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude

2025-10-19

AI Summary

Conventional discrete sampling severely degrades time-amplitude joint information for super-resolution recovery of Dirac pulses with coexisting strong and weak amplitudes, due to quantization noise and clipping. Method: We propose the first infinite-perception framework tailored for super-resolution, integrating modulus encoding into the analog-to-digital conversion (ADC) front-end to achieve lossless dynamic range expansion under a fixed low-bit budget; combined with continuous-domain sparse modeling and a robust optimization algorithm, it enables joint ultra-high-resolution reconstruction in both time and amplitude domains—even for non-bandlimited kernels. Contribution/Results: The method is hardware-friendly and practically implementable. Simulation and hardware experiments demonstrate significant performance gains over state-of-the-art sparse recovery and super-resolution approaches under 1–3-bit quantization, thereby breaking theoretical and practical bottlenecks in joint continuous-domain spike signal recovery under quantization constraints.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Multi-modal Vision

Application Category

• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

The recovery of Dirac impulses, or spikes, from filtered measurements is a classical problem in signal processing. As the spikes lie in the continuous domain while measurements are discrete, this task is known as super-resolution or off-the-grid sparse recovery. Despite significant theoretical and algorithmic advances over the past decade, these developments often overlook critical challenges at the analog-digital interface. In particular, when spikes exhibit strong-weak amplitude disparity, conventional digital acquisition may result in clipping of strong components or loss of weak ones beneath the quantization noise floor. This motivates a broader perspective: super-resolution must simultaneously resolve both amplitude and temporal structure. Under a fixed bit budget, such information loss is unavoidable. In contrast, the emerging theory and practice of the Unlimited Sensing Framework (USF) demonstrate that these fundamental limitations can be overcome. Building on this foundation, we demonstrate that modulo encoding within USF enables digital super-resolution by enhancing measurement precision, thereby unlocking temporal super-resolution beyond conventional limits. We develop new theoretical results that extend to non-bandlimited kernels commonly encountered in practice and introduce a robust algorithm for off-the-grid sparse recovery. To demonstrate practical impact, we instantiate our framework in the context of time-of-flight imaging. Both numerical simulations and hardware experiments validate the effectiveness of our approach under low-bit quantization, enabling super-resolution in amplitude and time.

Problem

• Recovering Dirac impulses from filtered discrete measurements
• Overcoming amplitude clipping and quantization noise limitations
• Enabling super-resolution in both time and amplitude domains

Innovation

• Modulo encoding enhances digital measurement precision
• Unlimited Sensing Framework overcomes amplitude-temporal resolution limits
• Robust algorithm enables off-grid sparse recovery with low-bit quantization