IMG-29

Contrast-to-noise ratio

CNR = |Sa − Sb| / σ. Two-region detectability.

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Image qualityCNR

Governing equation

\mathrm{CNR}=|S_a-S_b|/\sigma

$\sigma \in \left[1, 80\right]$

where

S_a: Signal A (HU)
S_b: Signal B (HU)
\sigma: Noise σ (HU)
CNR: Contrast-to-noise (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{CNR}=|S_a-S_b|/\sigma

$\sigma \in \left[1, 80\right]$

$\sigma = 1$ $CNR = 40$

Along the curve

②

Domain of the variable — blue

\sigma_{\min} = 1,\quad \sigma_{\max} = 80

$\sigma \in \left[1, 80\right]$

$\sigma = 1$ $\sigma = 1$

Along the curve

③

Response curve — green

\mathrm{CNR}=|S_a-S_b|/\sigma

$\sigma \in \left[1, 80\right]$

$\sigma = 1$ $CNR = 40$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}CNR}{\mathrm{d}\sigma}

$\sigma \in \left[1, 80\right]$

$\sigma = 1.497$ $CNR^{\prime} = -20.06$

Along the curve

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-29 — Contrast-to-noise ratio) is the form associated with CNR. Working symbols: $S_a$ , $S_b$ , $\sigma$ $\rightarrow$ $CNR$ . CNR, not SNR, decides whether a lesion pops from its background. Rose applies to CNR too.

Purpose

Purpose: compute

CNR

from

S_a

S_b

\sigma

in Medical imaging via

\mathrm{CNR}=|S_a-S_b|/\sigma

CNR = |Sa − Sb| / σ. Two-region detectability. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

S_a = 80.000\,\mathrm{HU}

S_b = 40.000\,\mathrm{HU}

\sigma = 12.000\,\mathrm{HU}

, the governing relation

\mathrm{CNR}=|S_a-S_b|/\sigma

yields

CNR = 3.33\,\mathrm{—}

. Two mean greys and a noise σ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Signal A S_a80 HUSignal B S_b40 HUNoise σ \sigma12 HU

Outputs

Contrast-to-noise CNR3.33 —

Reading speed

Watch on YouTube

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Narration of this film

Two mean greys and a noise σ.

CNR, not SNR, decides whether a lesion pops from its background. Rose applies to CNR too.

Reading speed

Watch on YouTube