IMG-16

Pixel bandwidth

BW_pix = BW_read / Nx. Hertz per pixel along readout.

Reading speed

MRIPixel bandwidth

Governing equation

BW_{\mathrm{pix}}=BW_{\mathrm{read}}/N_x

$BW_{read} \in \left[5000, 2.5\times 10^{5}\right]$

where

BW_{read}: Readout bandwidth (Hz)
N_x: Frequency encodes (—)
BW_{pix}: Pixel bandwidth (Hz/px)

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

BW_{\mathrm{pix}}=BW_{\mathrm{read}}/N_x

$BW_{read} \in \left[5000, 2.5\times 10^{5}\right]$

$BW_{read} = 5000$ $BW_{pix} = 19.53$

Along the curve

②

Domain of the variable — blue

BW_{read}_{\min} = 5000,\quad BW_{read}_{\max} = 2.5\times 10^{5}

$BW_{read} \in \left[5000, 2.5\times 10^{5}\right]$

$BW_{read} = 5000$ $BW_{read} = 5000$

Along the curve

③

Response curve — green

BW_{\mathrm{pix}}=BW_{\mathrm{read}}/N_x

$BW_{read} \in \left[5000, 2.5\times 10^{5}\right]$

$BW_{read} = 5000$ $BW_{pix} = 19.53$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}BW_{pix}}{\mathrm{d}BW_{read}}

$BW_{read} \in \left[5000, 2.5\times 10^{5}\right]$

$BW_{read} = 6540.9$ $BW_{pix}^{\prime} = 0.004$

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-16 — Pixel bandwidth) is the form associated with Pixel bandwidth. Working symbols: $BW_{read}$ , $N_x$ $\rightarrow$ $BW_{pix}$ . Chemical-shift pixels = Δf / BW_pix. High BW_pix reduces shift but costs SNR.

Purpose

Purpose: compute

BW_{pix}

from

BW_{read}

N_x

in Medical imaging via

BW_{\mathrm{pix}}=BW_{\mathrm{read}}/N_x

BW_pix = BW_read / Nx. Hertz per pixel along readout. 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

BW_{read} = 50000.000\,\mathrm{Hz}

N_x = 256.000\,\mathrm{—}

, the governing relation

BW_{\mathrm{pix}}=BW_{\mathrm{read}}/N_x

yields

BW_{pix} = 195.3\,\mathrm{Hz/px}

. A readout window split into Nx bins. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Readout bandwidth BW_{read}50000 HzFrequency encodes N_x256 —

Outputs

Pixel bandwidth BW_{pix}195.3 Hz/px

Reading speed

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Narration of this film

A readout window split into Nx bins.

Chemical-shift pixels = Δf / BW_pix. High BW_pix reduces shift but costs SNR.

Reading speed

Watch on YouTube