Signal-to-Noise Ratio

What is Signal-to-Noise Ratio?

Signal-to-noise ratio (SNR) is a measure that compares the level of a desired signal to background noise. It is defined as the ratio of signal power to noise power, expressed in decibels (dB). A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.

SNR quantifies how useful information stands out from unwanted interference. The concept originated in electrical engineering but now applies across telecommunications, data analysis, imaging systems, and spectroscopy.

A high signal-to-noise ratio indicates strong signal relative to noise, allowing for clearer transmission or better image quality. Conversely, low SNR suggests noise may obscure important details.

Calculating Signal-to-Noise Ratio

The basic signal-to-noise ratio formula is:

SNR = P_signal / P_noise

Where:

• P_signal is the power of the signal
• P_noise is the power of the noise

Often, SNR is expressed in logarithmic decibel form:

SNR(dB) = 10 × log₁₀(P_signal / P_noise)

The signal-to-noise ratio calculation varies by application. In hyperspectral imaging, SNR is typically determined for each spectral band by comparing the response to a uniform target against the standard deviation of noise in that band.

For precise characterisation, SNR must be measured under controlled conditions with calibrated targets and standardised lighting.

Signal-to-Noise Ratio vs Noise-Equivalent-Spectral-Radiance

While SNR provides a relative measure of signal quality, NESR (noise equivalent spectral radiance) offers an absolute metric for specifying the sensitivity of a spectral imaging system. NESR represents the minimum detectable radiance difference at a specific wavelength, defining the detection threshold of the system.

The primary difference:

• SNR is a unitless ratio comparing signal strength to noise
• Noise equivalent spectral radiance is expressed in physical units (W/m²/sr/nm) representing the minimum detectable signal

A system with low NESR values can detect fainter signals, while a high SNR system produces cleaner measurements at normal operating levels.

How SNR and NESR impact imagery

In hyperspectral imagery, SNR directly influences:

1. Spatial resolution – Higher SNR allows finer spatial details to be resolved
2. Spectral resolution – Better SNR enables discrimination between similar spectral signatures
3. Classification accuracy – Higher SNR leads to more reliable material categorisation
4. Detection limits – Lower NESR values correspond to improved ability to detect trace materials

Systems with superior SNR performance produce imagery with greater clarity and enhanced ability to detect subtle features. Living Optics has developed a VIS-NIR video-rate hyperspectral imaging camera that captures both spatial and spectral information in real-time at video frame rates. Their technology aims to make hyperspectral imaging more accessible by tackling challenges that have limited its adoption in many industries.

In quality control, pharmaceutical verification, or environmental monitoring, these improvements can be crucial. Living Optics’ camera generates a 2048 x 2432 pixel RGB image with 4384 hyperspectral sampling points, each consisting of 96 bands across the 440-990nm spectral range. For more detailed information resolution, see Living Optics’ guide on spectral resolution.

How SNR can be improved by frame averaging of video data

Frame averaging is an effective technique for improving SNR in hyperspectral systems. By capturing multiple frames of the same scene and averaging them, random noise can be reduced while preserving signal information.

The SNR improvement follows:

SNR_improved = SNR_single × √N

Where N is the number of frames averaged.

This means averaging 4 frames improves SNR by 2×, while 16 frames improves it by 4×. Practical limitations include:

• Motion artefacts if the subject moves during capture
• Diminishing returns as frame counts increase
• Processing overhead for large datasets
• Longer effective exposure times

Living Optics has developed a camera capable of capturing up to 30 hyperspectral frames per second, making it suitable for frame averaging techniques. Their system uses snapshot spectral technology rather than traditional line-scanning methods, allowing for instantaneous capture of the entire scene and avoiding motion blur that affects conventional systems.

FAQs

How does SNR relate to image quality in hyperspectral systems?

Higher SNR directly correlates with improved image quality, allowing clearer visualisation of spectral information and more reliable analysis.

What’s more important, high SNR or low NESR?

It depends on the application. For detecting very faint signals, NESR is often more critical. For precision measurements, SNR typically takes precedence.

Can software improve SNR after image capture?

Yes, denoising algorithms can enhance SNR post-capture, but cannot recover information completely lost in noise. The best results come from optimising SNR during acquisition.