Unlimited Sensing: When Noise Becomes the Signal

Source: SIAM News — Ayush Bhandari, Imperial College London

TL;DR

Unlimited sensing is a novel approach that harnesses quantization noise from traditional digitization methods to achieve clearer sensing. Instead of clipping signals that exceed conventional sensor range, the method uses "folding" — when the signal exceeds the sensor's range, it folds back rather than being clipped, preserving information that would otherwise be lost. This allows sensors to capture signals far beyond their nominal range without hardware modifications. The technique has evolved from theoretical concept to practical applications with implications for various sensing modalities.

The Fundamental Problem: Dynamic Range

Every sensor has a limited dynamic range — the range of signal intensities it can measure before saturating or clipping. When a signal exceeds this range, traditional sensors either:

• Clip — Truncate the signal at the maximum value, losing all information about the true magnitude
• Saturate — Become non-responsive, providing no useful data until the signal drops back into range

This is a fundamental limitation: you can increase the dynamic range by building better hardware (more sensitive detectors, larger bit-depth ADCs), but this is expensive, power-hungry, and ultimately bounded by physics. A different approach is needed.

The Unlimited Sensing Solution: Folding

Unlimited sensing takes a radically different approach. Instead of trying to build sensors with larger dynamic range, it modifies the sensing process so that information about high-amplitude signals is preserved even within the sensor's existing constraints.

The key mechanism is folding: when a signal exceeds the sensor's range, it folds back rather than clipping. Think of it like folding a piece of paper — the signal continues to exist, but it's mapped back into the sensor's measurement range via a folding transformation.

How Folding Works

1. The input signal exceeds the sensor's nominal range
2. Instead of clipping, the sensor "folds" the excess — the output wraps around from the measurement ceiling back to the floor (or vice versa)
3. The folding pattern encodes information about the original signal's amplitude
4. A reconstruction algorithm recovers the original signal from the folded measurements

This is mathematically analogous to modulo sampling — measuring the signal modulo the sensor's dynamic range. The measurement y is related to the input x by:

y = x mod R

Where R is the sensor's range. For signals that fit within the range (no folding), this is just normal sensing. For signals that exceed the range, the modulo operation preserves information that would be lost to clipping.

From Theory to Practice

Unlimited sensing was initially a theoretical concept in signal processing and information theory. The key questions were:

1. Uniqueness — Can the original signal be uniquely recovered from folded measurements?
2. Stability — Is the recovery robust to noise?
3. Algorithms — Can we design efficient reconstruction algorithms?

These questions have been largely resolved. The mathematical foundations show that, under reasonable assumptions (e.g., bandlimited signals, finite rate of innovation), the original signal can be uniquely and stably recovered from folding measurements. Reconstruction algorithms based on unwrapping, phase retrieval, and optimization techniques have been developed and refined.

The approach has now moved from theory to hardware prototypes and practical applications.

Advantages Over Traditional Approaches

Aspect	Traditional Clipping	Unlimited Sensing (Folding)
High-amplitude signals	Information lost	Information preserved
Hardware cost	Expensive (need larger range)	Same hardware, no modifications
Power consumption	Higher (more bits, more power)	Same or lower
Dynamic range improvement	Requires hardware upgrade	10x–100x via software

The most compelling advantage: no hardware modifications are needed. Existing sensors can achieve vastly larger effective dynamic ranges simply by changing the readout strategy and the reconstruction software.

Implications for Sensing Modalities

Unlimited sensing has implications across many sensing domains:

Imaging

High dynamic range (HDR) imaging without specialized HDR sensors. Standard cameras can capture scenes with extreme contrast ratios — bright sunlight and deep shadows simultaneously — without the blooming or saturation artifacts that plague conventional imaging.

Audio and Acoustics

Microphones can capture sound pressure levels far beyond their nominal rating. This is particularly valuable for: - Gunshot and explosion monitoring - Industrial acoustic monitoring - Wildlife audio (close-proximity animal calls)

Electrical and Biomedical Sensors

Oscilloscopes and biomedical sensors (EEG, ECG) can capture signals with large dynamic variations without gain-switching or range-setting — simplifying device design and reducing artifacts from range transitions.

Radar and Lidar

Reflected signals with enormous dynamic range variations (strong returns from nearby objects, weak returns from distant ones) can be captured in a single measurement without saturation.

Key Takeaways

• Unlimited sensing uses folding (modulo sampling) instead of clipping when signals exceed sensor range
• The folding preserves information that would be lost in traditional clipping or saturation approaches
• No hardware modifications needed — existing sensors can achieve 10x–100x effective dynamic range increases
• Theoretical foundations (uniqueness, stability, reconstruction algorithms) are well established
• Applications span imaging, audio, biomedical sensing, radar, and lidar
• Developed primarily by Ayush Bhandari and colleagues at Imperial College London
• Represents a paradigm shift: instead of fighting noise (quantization error), harness it as signal