Glossary
155 abbreviations used across the modules. In the modules, the first use of a term in each section is underlined with dots: hover, tap or press Enter on it to see the definition.
A B C D E F G H I K L M N O P Q R S T U V W
- AAF anti-aliasing filter
Analog low-pass filter before the ADC that removes content above half the sampling rate.
Module 03 · Convolution, LTI & filters - ABCD ABCD (transmission) matrix
Two-port representation that chains layers by matrix multiplication.
Module 16 · Piezoelectrics & KLM - ADC analog-to-digital converter
Converts the amplified analog echo into samples.
Module 20 · Front-end electronics - ADMIRE aperture domain model image reconstruction
Model-based beamformer that fits channel data with a set of modelled wavefronts and keeps only the components from the region of interest.
Module 25 · Adaptive & coherence BF - ADMM alternating direction method of multipliers
Splits an optimization into simpler sub-problems that are solved in turn and tied together by dual variables.
Module 13 · Inverse problems - AIUM American Institute of Ultrasound in Medicine
Professional society that issues safety and practice statements.
Module 22 · Acoustic output & safety - ALARA as low as reasonably achievable
Safety principle: use the lowest output and shortest exposure that answer the clinical question.
Module 22 · Acoustic output & safety - AlN aluminium nitride
Thin-film piezoelectric used in PMUTs; CMOS-compatible.
Module 18 · CMUT, PMUT & new materials - AM amplitude modulation
Contrast or harmonic pulse sequence that combines transmits of different amplitudes so linear echoes cancel.
Module 15 · Wave physics & harmonics - AR autoregressive (model)
Model in which each sample is a weighted sum of past samples plus white noise; used for spectral estimation and prediction.
Module 27 · Spectral estimation & QUS - ARFI acoustic radiation force impulse
Imaging of tissue displacement caused by a long focused push pulse.
Module 30 · Elastography - ASIC application-specific integrated circuit
Custom chip, for example the in-probe electronics of a matrix array.
Module 19 · Arrays: 1D to 2D, RCA, CMUT - BIBO bounded-input bounded-output
Stability criterion: every bounded input gives a bounded output. For LTI systems, the impulse response must be absolutely summable.
Module 03 · Convolution, LTI & filters - BSC backscatter coefficient
Backscattered power per unit volume, solid angle and incident intensity; frequency dependence carries scatterer size.
Module 27 · Spectral estimation & QUS - BVD Butterworth–Van Dyke model
Lumped equivalent circuit (static capacitance in parallel with a series RLC) of a resonator near resonance.
Module 20 · Front-end electronics - BW bandwidth
Width of the frequency band a signal or system occupies, usually defined at −3 or −6 dB.
Module 04 · Sampling, Fourier, LTI - CEM43 cumulative equivalent minutes at 43 °C
Thermal dose: heating converted to the equivalent time at 43 °C.
Module 22 · Acoustic output & safety - CEUS contrast-enhanced ultrasound
Imaging with gas microbubble contrast agents.
Module 28 · Microbubbles & contrast - CF coherence factor
Ratio of coherent to incoherent energy across the aperture; used as a pixel weight that suppresses clutter.
Module 25 · Adaptive & coherence BF - CFL Courant–Friedrichs–Lewy condition
Stability limit on the time step of explicit wave solvers: c·Δt/Δx must stay below a constant.
Module 21 · Simulation & characterization - CGLS conjugate gradient for least squares
Krylov method that solves least squares without forming AᴴA; stopping early acts as regularization.
Module 13 · Inverse problems - CIC cascaded integrator–comb
A multiplier-free filter structure used for large decimation factors.
Module 09 · Digital filter design - CMA common mid-angle
CUTE refinement (Stähli et al. 2020) that compares transmit/receive angle pairs sharing the same mid-angle; these sample the same k-space region, so their speckle stays correlated and the phase difference reflects sound-speed error.
Module 32 · Sound-speed estimation - CMOS complementary metal–oxide–semiconductor
The standard integrated-circuit process; CMUTs and PMUTs can be built on top of it.
Module 18 · CMUT, PMUT & new materials - CMUT capacitive micromachined ultrasonic transducer
Transducer made of thin vibrating membranes over vacuum gaps, built with silicon micromachining.
Module 18 · CMUT, PMUT & new materials - CNR contrast-to-noise ratio
Difference of mean intensities inside and outside a target, divided by a noise or speckle measure.
Module 26 · Speckle statistics - CPS contrast pulse sequence
Multi-pulse sequence combining amplitude and phase changes to isolate nonlinear microbubble echoes.
Module 28 · Microbubbles & contrast - CR contrast ratio
Ratio of mean intensities inside and outside a target, usually in dB.
Module 26 · Speckle statistics - CRLB Cramér–Rao lower bound
Lower bound on the variance of any unbiased estimator, given by the inverse Fisher information.
Module 12 · Estimation & CRLB - CTR contrast-to-tissue ratio
Microbubble signal relative to the residual tissue signal after contrast processing, in dB.
Module 28 · Microbubbles & contrast - CUTE computed ultrasound tomography in echo mode
Estimates a sound-speed map from phase shifts between images beamformed at different transmit/receive angles.
Module 32 · Sound-speed estimation - CW continuous wave
Transmission without pulses; gives Doppler without range resolution.
Module 29 · Doppler & flow - DAC digital-to-analog converter
Converts digital values into an analog voltage.
Module 20 · Front-end electronics - DAS delay-and-sum
Beamforming by delaying each channel to align echoes from a point, then summing; the reference method.
Module 23 · Beams, k-space, compounding - DC direct current (zero frequency)
The zero-frequency (mean) component of a signal.
Module 02 · The DFT and FFT by hand - DFT discrete Fourier transform
Maps N samples to N complex frequency coefficients; the finite, sampled version of the Fourier transform.
Module 02 · The DFT and FFT by hand - DMAS delay-multiply-and-sum
Nonlinear beamformer that sums products of channel pairs after delay.
Module 25 · Adaptive & coherence BF - DOF depth of field
Axial range over which a focused beam stays near its focal width.
Module 23 · Beams, k-space, compounding - DORT decomposition of the time-reversal operator
Eigen-analysis of the inter-element response matrix; for well-resolved point scatterers, each strong singular vector focuses on one scatterer.
Module 06 · Eigen & SVD - DPSS discrete prolate spheroidal sequences
Slepian tapers that maximize energy concentration in a band; the windows of the multitaper method.
Module 27 · Spectral estimation & QUS - DSPC distearoylphosphatidylcholine
A lipid commonly used in microbubble shells.
Module 28 · Microbubbles & contrast - DTFT discrete-time Fourier transform
Fourier transform of an infinite discrete-time sequence; a continuous, 2π-periodic function of frequency. The DFT samples it.
Module 02 · The DFT and FFT by hand - ENBW equivalent noise bandwidth
Width of an ideal rectangular filter passing the same white-noise power as a given window or filter.
Module 02 · The DFT and FFT by hand - ENOB effective number of bits
Resolution an ADC actually delivers once noise and distortion are counted.
Module 20 · Front-end electronics - ENR energy-to-noise ratio
Signal energy divided by noise power spectral density; sets the CRLB for delay and localization.
Module 12 · Estimation & CRLB - ESBMV eigenspace-based minimum variance
MV beamformer whose weights are projected onto the signal subspace of the covariance matrix.
Module 25 · Adaptive & coherence BF - ESD effective scatterer diameter
Scatterer size estimated by fitting a form factor to the frequency dependence of the BSC.
Module 27 · Spectral estimation & QUS - FBW fractional bandwidth
Bandwidth divided by centre frequency, often at −6 dB.
Module 04 · Sampling, Fourier, LTI - FD finite difference
Approximating derivatives by differences on a grid.
Module 21 · Simulation & characterization - FDA US Food and Drug Administration
US regulator for medical devices, including ultrasound output limits.
Module 22 · Acoustic output & safety - FDTD finite-difference time-domain
Numerical wave simulation on a grid, stepping fields forward in time.
Module 21 · Simulation & characterization - FEA finite element analysis
Simulation using the finite element method.
Module 17 · Matching, backing, lens, FEA - FEM finite element method
Numerical solution of field equations on a mesh of small elements.
Module 17 · Matching, backing, lens, FEA - FFT fast Fourier transform
An O(N log N) algorithm that computes the DFT.
Module 02 · The DFT and FFT by hand - FIR finite impulse response
A digital filter whose impulse response has finite length; always stable and can have exactly linear phase.
Module 09 · Digital filter design - FISTA fast ISTA
ISTA with Nesterov momentum; the objective error falls as O(1/k²) instead of ISTA's O(1/k) (Beck & Teboulle 2009).
Module 13 · Inverse problems - FPGA field-programmable gate array
Reconfigurable chip used for beamforming and data handling.
Module 20 · Front-end electronics - FRC Fourier ring correlation
Resolution measure from the correlation of two independent half-images over rings in k-space.
Module 31 · ULM end to end - FWHM full width at half maximum
Width of a peak at half its maximum (−6 dB for amplitude); the usual resolution measure.
Module 23 · Beams, k-space, compounding - FWI full-waveform inversion
Estimates a sound-speed map by fitting full simulated waveforms to measured data.
Module 14 · Optimization & autodiff - FXPF f-x prediction filtering
Suppresses incoherent clutter by predicting each channel from its neighbours in the frequency–space domain.
Module 25 · Adaptive & coherence BF - GCF generalized coherence factor
Coherence factor that counts low spatial frequencies across the aperture as coherent energy.
Module 25 · Adaptive & coherence BF - gCNR generalized contrast-to-noise ratio
1 minus the overlap of the intensity distributions inside and outside a target; ranges from 0 to 1 and is unchanged by monotonic transforms such as log compression (Rodriguez-Molares et al. 2020).
Module 26 · Speckle statistics - GCV generalized cross-validation
Rule for choosing a regularization parameter by predicting held-out error without re-fitting.
Module 13 · Inverse problems - GD gradient descent
Iterative minimization by stepping against the gradient.
Module 14 · Optimization & autodiff - HV high voltage
Transmit supply voltage, typically tens of volts up to about ±100 V (some systems higher).
Module 20 · Front-end electronics - IEC International Electrotechnical Commission
Standards body whose standards define acoustic output measurement and safety for ultrasound.
Module 22 · Acoustic output & safety - IFFT inverse fast Fourier transform
The fast algorithm for the inverse DFT.
Module 24 · Fourier beamforming - IIR infinite impulse response
A recursive digital filter whose impulse response never ends; cheaper than FIR for sharp responses but can be unstable and has nonlinear phase.
Module 09 · Digital filter design - IQ in-phase/quadrature (complex baseband)
Complex signal obtained by mixing RF down to baseband and low-pass filtering; I is the real part, Q the imaginary part.
Module 08 · Analytic signal & IQ - IRLS iteratively reweighted least squares
Solves non-quadratic fitting problems as a sequence of weighted least-squares problems.
Module 09 · Digital filter design - ISLR integrated sidelobe ratio
Energy in all sidelobes relative to the main-lobe energy, in dB.
Module 23 · Beams, k-space, compounding - ISPTA spatial-peak temporal-average intensity
Highest temporal-average intensity in the field; its derated value ISPTA.3 is limited by FDA to 720 mW/cm² for most applications, alongside MI ≤ 1.9.
Module 22 · Acoustic output & safety - ISTA iterative shrinkage-thresholding algorithm
Proximal-gradient method for L1-regularized problems: a gradient step, then soft thresholding.
Module 13 · Inverse problems - IVUS intravascular ultrasound
Imaging from a catheter inside a blood vessel.
Module 18 · CMUT, PMUT & new materials - KLM Krimholtz–Leedom–Matthaei model
Equivalent circuit of a thickness-mode transducer as an acoustic transmission line coupled to an electrical port.
Module 16 · Piezoelectrics & KLM - KZK Khokhlov–Zabolotskaya–Kuznetsov equation
Parabolic model of nonlinear, diffracting, absorbing sound beams.
Module 15 · Wave physics & harmonics - LFM linear frequency modulation (chirp)
A pulse whose instantaneous frequency sweeps linearly in time; compressed by a matched filter.
Module 10 · Matched filtering - LM Levenberg–Marquardt
Damped Gauss–Newton method that moves between Gauss–Newton and gradient descent.
Module 14 · Optimization & autodiff - LNA low-noise amplifier
First receive amplifier; sets most of the system noise figure.
Module 20 · Front-end electronics - LPF low-pass filter
Passes frequencies below a cut-off and attenuates those above.
Module 08 · Analytic signal & IQ - LS least squares
Choosing parameters that minimize the sum of squared residuals.
Module 05 · Matrices as operators - LTI linear time-invariant
A system whose response to a weighted sum of inputs is the same weighted sum of the responses, and whose behaviour does not change over time; fully described by its impulse response.
Module 03 · Convolution, LTI & filters - MAP maximum a posteriori
Estimate that maximizes the posterior: likelihood times prior.
Module 12 · Estimation & CRLB - MI mechanical index
Derated (0.3 dB/cm/MHz) peak rarefactional pressure in MPa divided by the square root of the acoustic working frequency in MHz; indicates the likelihood of inertial cavitation (FDA limit 1.9).
Module 22 · Acoustic output & safety - MLE maximum-likelihood estimator
The parameter value that makes the observed data most probable.
Module 12 · Estimation & CRLB - MMSE minimum mean squared error
Estimator that minimizes the expected squared error; the posterior mean.
Module 12 · Estimation & CRLB - MOSFET metal–oxide–semiconductor field-effect transistor
The switching transistor of pulsers and multiplexers.
Module 20 · Front-end electronics - MRayl megarayl
Unit of acoustic impedance, 10⁶ kg/(m²·s). Soft tissue is about 1.5 MRayl, PZT about 34.
Module 17 · Matching, backing, lens, FEA - MSE mean squared error
Average squared estimation error; variance plus squared bias.
Module 12 · Estimation & CRLB - MTT mean transit time
Mean time contrast takes to pass through the tissue; a perfusion parameter from the TIC.
Module 28 · Microbubbles & contrast - MV minimum variance (Capon) beamformer
Adaptive beamformer that minimizes output power while keeping unit gain in the look direction.
Module 25 · Adaptive & coherence BF - MVDR minimum variance distortionless response
Another name for the minimum-variance (Capon) beamformer.
Module 07 · Covariance & correlation - NCC normalized cross-correlation
Cross-correlation of mean-removed signals divided by the square root of the product of their energies, so it lies between −1 and 1; the standard similarity measure for speckle tracking.
Module 11 · Correlation & delay - NF noise figure
Degradation of SNR through a stage, in dB.
Module 20 · Front-end electronics - NN neural network
Learned model built from layers of weighted sums and nonlinearities.
Module 31 · ULM end to end - OVL overlap (of histograms)
Area shared by the inside and outside intensity distributions; gCNR = 1 − OVL.
Module 26 · Speckle statistics - PALA Performance benchmarking of microbubble-localization algorithms
Open ULM benchmark (Heiles et al. 2022) with shared data and metrics.
Module 31 · ULM end to end - PCA principal component analysis
Finding the directions of largest variance; the SVD of centred data.
Module 06 · Eigen & SVD - PCF phase coherence factor
Weight based on the spread of channel phases instead of amplitudes.
Module 25 · Adaptive & coherence BF - PD power Doppler
Image of the Doppler signal power after clutter filtering, regardless of velocity.
Module 29 · Doppler & flow - PI pulse inversion
Two transmits of opposite polarity are summed so linear echoes cancel and even harmonics remain.
Module 15 · Wave physics & harmonics - PICMUS Plane-wave Imaging Challenge in Medical Ultrasound
IUS 2016 challenge that released shared plane-wave datasets and metrics for comparing beamformers.
Module 25 · Adaptive & coherence BF - PII pulse intensity integral
Time integral of instantaneous intensity over one pulse.
Module 22 · Acoustic output & safety - PML perfectly matched layer
Absorbing boundary layer that stops reflections at the edge of a simulation grid.
Module 21 · Simulation & characterization - PMN-PT lead magnesium niobate–lead titanate
Relaxor single crystal with higher coupling than PZT; used in wide-band probes.
Module 16 · Piezoelectrics & KLM - PMUT piezoelectric micromachined ultrasonic transducer
Micromachined plate transducer driven by a thin piezoelectric film.
Module 18 · CMUT, PMUT & new materials - PPW points per wavelength
Grid samples per wavelength in a simulation; too few cause numerical dispersion.
Module 21 · Simulation & characterization - PRF pulse repetition frequency
Number of transmit events per second; sets the Doppler Nyquist limit and the maximum imaging depth.
Module 29 · Doppler & flow - PRI pulse repetition interval
Time between transmit events; 1/PRF.
Module 10 · Matched filtering - PSD power spectral density
Distribution of a random signal's power over frequency; the Fourier transform of its autocorrelation.
Module 07 · Covariance & correlation - PSF point spread function
Image of a single point scatterer; sets resolution and sidelobe levels.
Module 23 · Beams, k-space, compounding - PSL peak sidelobe level
Highest sidelobe relative to the main lobe, in dB, for a beam pattern or a compressed pulse.
Module 10 · Matched filtering - PVDF polyvinylidene fluoride
Flexible piezoelectric polymer with low impedance; common in hydrophones.
Module 16 · Piezoelectrics & KLM - PW pulsed wave
Doppler mode with pulsed transmission and a range gate.
Module 29 · Doppler & flow - PWI plane-wave imaging
Imaging with unfocused plane-wave transmits, often at several angles that are compounded.
Module 24 · Fourier beamforming - PZT lead zirconate titanate
The standard piezoelectric ceramic for medical transducers.
Module 16 · Piezoelectrics & KLM - QR QR decomposition
Factorization into an orthonormal Q and an upper-triangular R; a stable way to solve least squares.
Module 05 · Matrices as operators - QUS quantitative ultrasound
Estimates tissue properties (attenuation, backscatter, scatterer size, speed of sound) as numbers rather than images.
Module 27 · Spectral estimation & QUS - RCA row–column addressed array
2D array whose elements are addressed through whole rows or whole columns (e.g. rows on transmit, columns on receive), so N+N channels serve an N×N aperture.
Module 19 · Arrays: 1D to 2D, RCA, CMUT - REFoCUS retrospective encoding for conventional ultrasound sequences
Decodes the transmit sequence from channel data so any transmit set can be refocused like synthetic aperture data.
Module 24 · Fourier beamforming - RF radio frequency (RF data)
The raw, real-valued echo signal around the transducer centre frequency, sampled above its Nyquist rate (typically 4× the centre frequency or more), before demodulation to IQ.
Module 08 · Analytic signal & IQ - RMB Reed–Mallett–Brennan rule
Result that a sample covariance from about 2N snapshots costs roughly 3 dB of SINR in an N-element adaptive beamformer.
Module 07 · Covariance & correlation - RMSE root-mean-square error
Square root of the MSE, in the units of the quantity.
Module 12 · Estimation & CRLB - ROI region of interest
Image region selected for measurement or processing.
Module 26 · Speckle statistics - SAFT synthetic aperture focusing technique
Imaging that focuses every pixel by combining many single-element or small-aperture transmits.
Module 24 · Fourier beamforming - ScAlN scandium aluminium nitride
AlN alloyed with scandium for a larger piezoelectric coefficient.
Module 18 · CMUT, PMUT & new materials - SCF sign coherence factor
Weight based on the agreement of channel signs (polarity).
Module 25 · Adaptive & coherence BF - SGD stochastic gradient descent
Gradient descent using noisy gradients from random subsets of the data.
Module 14 · Optimization & autodiff - SINR signal-to-interference-plus-noise ratio
Signal power divided by interference plus noise power; the figure of merit for adaptive beamformers.
Module 07 · Covariance & correlation - SIR spatial impulse response
Velocity potential at a field point produced by an impulsive normal velocity of the transducer face; the pressure is ρ₀ times the time derivative of the excitation convolved with it.
Module 21 · Simulation & characterization - SLD spectral log difference
Attenuation estimate from the log ratio of power spectra from two depths in a homogeneous region; its slope versus frequency, divided by 4Δz, gives the attenuation coefficient slope (Np/cm/MHz).
Module 27 · Spectral estimation & QUS - SLSC short-lag spatial coherence
Image formed from the spatial coherence of channel signals at small element lags, not from echo amplitude.
Module 25 · Adaptive & coherence BF - SMI sample matrix inversion
Adaptive beamforming that inverts the measured sample covariance matrix.
Module 07 · Covariance & correlation - SNR signal-to-noise ratio
Ratio of signal power to noise power, usually in dB. Sets detectability and the precision of every estimate in the course.
Module 10 · Matched filtering - SoS speed of sound
Propagation speed of sound in the medium; about 1540 m/s is the usual soft-tissue assumption.
Module 32 · Sound-speed estimation - SPTA spatial-peak temporal-average
Short for spatial-peak temporal-average intensity (ISPTA).
Module 22 · Acoustic output & safety - STFT short-time Fourier transform
Fourier transforms of short, windowed, usually overlapping segments, giving a time–frequency picture.
Module 25 · Adaptive & coherence BF - SVD singular value decomposition
Factorization A = UΣVᴴ into orthonormal bases and non-negative singular values; the tool behind clutter filtering, conditioning and regularization.
Module 06 · Eigen & SVD - SWE shear wave elastography
Measures shear-wave speed to estimate tissue stiffness.
Module 30 · Elastography - TB time–bandwidth product
Code duration times bandwidth; approximately the compression ratio, and the SNR gain of pulse compression relative to a short pulse of equal peak amplitude.
Module 10 · Matched filtering - TEE transesophageal echocardiography
Cardiac imaging with a probe placed in the oesophagus.
Module 19 · Arrays: 1D to 2D, RCA, CMUT - TGC time-gain compensation
Gain that increases with echo time to offset attenuation.
Module 20 · Front-end electronics - TI thermal index
Ratio of the relevant (attenuated, bounded) acoustic power to the power that raises a model tissue by 1 °C; an exposure indicator, not a measured temperature rise.
Module 22 · Acoustic output & safety - TIB bone thermal index
TI with bone at or near the focus.
Module 22 · Acoustic output & safety - TIC time–intensity curve
Echo intensity in an ROI versus time after contrast injection.
Module 28 · Microbubbles & contrast - TIS soft-tissue thermal index
TI for soft tissue only.
Module 22 · Acoustic output & safety - TOF time of flight
Arrival-time method, e.g. estimating shear-wave speed from arrival times at several lateral positions.
Module 30 · Elastography - TSVD truncated SVD
Regularization that keeps only the largest singular values when inverting.
Module 06 · Eigen & SVD - TTP time to peak
Time from arrival (or injection) to the TIC maximum.
Module 28 · Microbubbles & contrast - TV total variation
Regularizer equal to the sum of gradient magnitudes; it favours piecewise-constant images with sharp edges.
Module 13 · Inverse problems - ULM ultrasound localization microscopy
Super-resolution imaging that localizes and tracks individual microbubbles over many frames.
Module 31 · ULM end to end - VCZ van Cittert–Zernike (theorem)
For diffuse scatterers, the spatial coherence of echoes across the receive aperture is the Fourier transform of the insonified intensity distribution; at the transmit focus it equals the autocorrelation of the transmit apodization.
Module 07 · Covariance & correlation - VGA variable-gain amplifier
Amplifier whose gain changes with depth to apply TGC.
Module 20 · Front-end electronics - WSS wide-sense stationary
A random process whose mean is constant and whose covariance depends only on the time difference.
Module 07 · Covariance & correlation