IMG-28

Rose criterion

SNR = C √n ≥ k. Detection needs about k ≈ 5.

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Image qualityRose 1948

Governing equation

\mathrm{SNR}=C\sqrt{n}\ge k

$n \in \left[50, 1\times 10^{6}\right]$

where

C: Contrast C (—)
n: Quanta in object (—)
k: Rose threshold k (—)
SNR: Rose SNR (—)
SNR/k: Detectability ratio (—)

The figure, part by part

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①

Governing law — red

\mathrm{SNR}=C\sqrt{n}\ge k

$n \in \left[50, 1\times 10^{6}\right]$

$n = 50$ $SNR = 0.707$

Along the curve

②

Domain of the variable — blue

n_{\min} = 50,\quad n_{\max} = 1\times 10^{6}

$n \in \left[50, 1\times 10^{6}\right]$

$n = 50$ $n = 50$

Along the curve

③

Response curve — green

\mathrm{SNR}=C\sqrt{n}\ge k

$n \in \left[50, 1\times 10^{6}\right]$

$n = 50$ $SNR = 0.707$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}SNR}{\mathrm{d}n}

$n \in \left[50, 1\times 10^{6}\right]$

$n = 6339$ $SNR^{\prime} = 8.37\times 10^{-4}$

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-28 — Rose criterion) is the form associated with Rose 1948. Working symbols: $C$ , $n$ , $k$ $\rightarrow$ $SNR$ , $SNR/k$ . C is subject contrast, n the number of quanta in the object area. Rose's k is empirical ~4–5.

Purpose

Purpose: compute

SNR

SNR/k

from

C

n

k

in Medical imaging via

\mathrm{SNR}=C\sqrt{n}\ge k

SNR = C √n ≥ k. Detection needs about k ≈ 5. 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

C = 0.100\,\mathrm{—}

n = 2500.000\,\mathrm{—}

k = 5.000\,\mathrm{—}

, the governing relation

\mathrm{SNR}=C\sqrt{n}\ge k

yields

SNR = 5.00\,\mathrm{—}

SNR/k = 1.00\,\mathrm{—}

. A disc on a noisy background, a detectability bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Contrast C C0.1 —Quanta in object n2500 —Rose threshold k k5 —

Outputs

Rose SNR SNR5.00 —
Detectability ratio SNR/k1.00 —

Reading speed

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Narration of this film

A disc on a noisy background, a detectability bar.

C is subject contrast, n the number of quanta in the object area. Rose's k is empirical ~4–5.

Reading speed

Watch on YouTube