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Figure of merit for analog-to-digital conversion
Mean square quantization error (MSQE) is a figure of merit for the process of analog to digital conversion. In this conversion process, analog signals
Mean square quantization error
Mean_square_quantization_error
Measure of the error of an estimator
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures
Mean_squared_error
Process of mapping a continuous set to a countable set
{\displaystyle \Delta ^{2}/12} . Mean squared error is also called the quantization noise power. Adding one bit to the quantizer halves the value of Δ, which
Quantization (signal processing)
Quantization_(signal_processing)
deformation like coordinate-wise power before projection, reducing mean-squared quantization error by ~10%. PVQ is used in the CELT audio codec (inherited into
Pyramid_vector_quantization
Performance measure of a digital radio
actual received symbols and ideal symbols. The root mean square (RMS) average amplitude of the error vector, normalized to ideal signal amplitude reference
Error_vector_magnitude
Online vector quantization algorithm
searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction
TurboQuant
Smallest value a measuring instrument can measure
arithmetic mean of the result, the mean value would be very close to the true value of the measured quantity. William Woolsey Johnson The Theory of Errors and
Least_count
Ratio of the desired signal to the background noise
minimum possible noise level is the error caused by the quantization of the signal, sometimes called quantization noise. This noise level is non-linear
Signal-to-noise_ratio
Measure of performance in digital-to-analog and analog-to-digital converters
alternatively the mean squared) INL. While the INL can be measured for every possible input/output code, often only the maximal error is provided when
Integral_nonlinearity
Vector quantization algorithm minimizing the sum of squared deviations
(squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors
K-means_clustering
modulation error ratio is equal to the ratio of the root mean square (RMS) power (in Watts) of the reference vector to the power (in Watts) of the error. It
Modulation_error_ratio
difference Mean square quantization error Mean square weighted deviation Mean squared error Mean squared prediction error Mean time between failures Mean-reverting
List_of_statistics_articles
Theory about lossy data compression
defined as the expected value of the square of the difference between input and output signal (i.e., the mean squared error). However, since we know that most
Rate–distortion_theory
Overview of and topical guide to machine learning
regularization Matthews correlation coefficient Mean shift Mean squared error Mean squared prediction error Measurement invariance Medoid MeeMix Melomics
Outline_of_machine_learning
Known channel properties of a communication link
between these two levels; instantaneous CSI with some estimation/quantization error is combined with statistical information. In a narrowband flat-fading
Channel_state_information
Statistical method of dividing data into equal-sized intervals for analysis
least squares, in which the sum of the absolute value of the observed errors is used in place of the squared error. The connection is that the mean is the
Quantile
Unit of measurement for amplitude levels in digital systems
the signal before sampling. This removes the effects of non-uniform quantization error, but increases the minimum noise floor. The phrase "dB below full
DBFS
Quantum mechanical operator related to rotational symmetry
{\displaystyle \hbar } is reduced Planck constant: A common way to derive the quantization rules above is the method of ladder operators. The ladder operators for
Angular_momentum_operator
American electrical engineer (1929–2025)
Prentice-Hall, Inc., 1994. 2008 B. Widrow and I. Kollar. Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications
Bernard_Widrow
quality level. The deviation from the source is usually measured as the mean squared error, in order to maximize the PSNR video quality metric. Calculating the
Rate–distortion_optimization
preserved along with the mean. AMBTC is computationally simpler than BTC and also typically results in a lower Mean Squared Error (MSE). AMBTC was proposed
Block_Truncation_Coding
Audio performance differences between technologies
uncorrelated quantization noise through the use of dither. The magnitude of this noise or distortion is determined by the number of quantization levels. In
Comparison of analog and digital recording
Comparison_of_analog_and_digital_recording
Uniform distribution on an interval
distributed random variables. In analog-to-digital conversion, a quantization error occurs. This error is either due to rounding or truncation. When the original
Continuous uniform distribution
Continuous_uniform_distribution
Random fluctuation in an electrical signal
a root mean square (RMS) voltage (identical to the noise standard deviation) in volts, dBμV or a mean squared error (MSE) in volts squared. Examples
Noise_(electronics)
Image compression standard and coding system
coefficients, so the output does not require rounding (quantization) and so it does not introduce any quantization noise. It is used in lossless coding. The wavelet
JPEG_2000
Artificial neural network algorithm
the learning rule of the network can be as simple as an XOR gate or mean squared error, or as complex as the result of a system of differential equations
Learning_rule
experiment: quantization should not have been observable. At least five years would elapse before this mystery was resolved: quantization was observed
History_of_quantum_mechanics
Non-mathematical introduction
summarized many other experimental findings. The quantization of the photoelectric effect and now the quantization of the electron orbits set the stage for the
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Statistical bias in linear regressions
with Frost and Thompson (2000). Errors-in-variables models Quantization (signal processing) – a common source of error in the explanatory or independent
Regression_dilution
Metric used to measure signal quality
known noise-free source image. PSNR is most easily defined via the mean squared error (MSE). Given a noise-free m×n monochrome image I and its noisy approximation
Peak_signal-to-noise_ratio
Technique to reduce dimensionality of points in Euclidean space
dimension even faster. Random projection can be further condensed by quantization (discretization), with 1-bit (sign random projection) or multi-bits.
Random_projection
Image denoising algorithm
compared with local mean algorithms. If compared with other well-known denoising techniques, non-local means adds "method noise" (i.e. error in the denoising
Non-local_means
Theory of quantum gravity merging quantum mechanics and general relativity
{E}}_{i}^{3}{\tilde {E}}^{3i}}}.} According to the rules of canonical quantization the triads E ~ i 3 {\displaystyle {\tilde {E}}_{i}^{3}} should be promoted
Loop_quantum_gravity
Motion video technology
into quantizers for direct application to a three-dimensional transformed block of the motion video sequence, followed by an inverse quantization (signal
ZPEG
Quasiparticle of mechanical vibrations
mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves
Phonon
Statistical law in machine learning
precision, recall, and F1 score for classification tasks; Mean squared error (MSE) or mean absolute error (MAE) for regression tasks; Elo rating in a competition
Neural_scaling_law
Use of multiple antennas in radio
minimum mean squared error (MMSE) algorithm detects the transmitted signals, x ~ {\displaystyle {\tilde {\mathbf {x} }}} , through minimizing the mean squared
MIMO
Process of removing noise from a signal
S2CID 62705333. Chervyakov, N. I.; Lyakhov, P. A.; Nagornov, N. N. (2018-11-01). "Quantization Noise of Multilevel Discrete Wavelet Transform Filters in Image Processing"
Noise_reduction
Tree-based ensemble machine learning methods
g. the following statistics can be used: Entropy Gini coefficient Mean squared error The normalized importance is then obtained by normalizing over all
Random_forest
Difficulties arising when analyzing data with many aspects ("dimensions")
PMID 21868861. S2CID 13086902. B. Chandrasekaran; A. K. Jain (1974). "Quantization Complexity and Independent Measurements". IEEE Transactions on Computers
Curse_of_dimensionality
Concept in information theory
calculation. The differential entropy yields a lower bound on the expected squared error of an estimator. For any random variable X {\displaystyle X} and estimator
Differential_entropy
photographic images Vector quantization: technique often used in lossy data compression TurboQuant: online vector quantization algorithm for lossy compression
List_of_algorithms
Means of quantifying system performance
each sample. Quantization, a process used in digital audio sampling, creates an error in the reconstructed signal. The Signal-to-quantization-noise ratio
Audio_system_measurements
Overview of and topical guide to deep learning
descent Adam optimization Learning rate Loss function Cross-entropy Mean squared error Regularization Dropout Early stopping Batch normalization Data augmentation
Outline_of_deep_learning
2018 open and royalty-free video coding format
vertical dimension (ext_tx). AV1 has new optimized quantization matrices (aom_qm). The eight sets of quantization parameters that can be selected and signaled
AV1
Kind of probability distribution
probability theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function
Generalized chi-squared distribution
Generalized_chi-squared_distribution
Conjecture on zeros of the zeta function
Michael Berry and Jonathan Keating conjectured that there is some unknown quantization H ^ {\displaystyle {\hat {H}}} of the classical Hamiltonian H = xp so
Riemann_hypothesis
Mathematical concept applicable to physics
dynamics Flux capacitor Flux footprint Flux pinning Flux quantization Gauss's law Inverse-square law Jansky (non SI unit of spectral flux density) Latent
Flux
Probability distribution
2012-07-04. Minguillon, J.; Pujol, J. (2001). "JPEG standard uniform quantization error modeling with applications to sequential and progressive operation
Laplace_distribution
Estimate of an unobservable underlying probability density function
accuracy. Frequency distribution Kernel density estimation Mean integrated squared error Histogram Multivariate kernel density estimation Spectral density
Density_estimation
integrand See also #Monte Carlo method Quantized state systems method (QSS) — based on the idea of state quantization Lebedev quadrature — uses a grid on
List of numerical analysis topics
List_of_numerical_analysis_topics
Visible interference in an image
noise. The noise caused by quantizing the pixels of a sensed image to a number of discrete levels is known as quantization noise. It has an approximately
Image_noise
Categorization of data using statistics
methodPages displaying short descriptions of redirect targets Learning vector quantization Linear classifier – Statistical classification in machine learning Fisher's
Statistical_classification
Mathematical transform that expresses a function of time as a function of frequency
treated as a separate harmonic oscillator and then quantized, a procedure known as "second quantization". Fourier methods have been adapted to also deal
Fourier_transform
Perceived video degradation
coefficient, Spearman's rank correlation coefficient, and the root mean square error (RMSE). Other metrics are the kappa coefficient and the outliers ratio
Video_quality
Dimensionless number that quantifies the strength of the electromagnetic interaction
value, but the error bars do not actually include zero. This result either indicates that α is not constant or that there is experimental error unaccounted
Fine-structure_constant
Function in quantum field theory showing probability amplitudes of moving particles
Verlag. ISBN 9783540875604. Greiner, W.; Reinhardt, J. (1996). Field Quantization. Springer Verlag. ISBN 9783540591795. Griffiths, D. J. (1987). Introduction
Propagator
Problem in information theory and communication
design. Several quantizer designs have been proposed, such as a nested lattice quantizer, trellis code quantizer and Lloyd quantization method. Unfortunately
Distributed_source_coding
Features that do not change if length or energy scales are multiplied by a common factor
exponential dispersion models, a class of statistical models used to describe error distributions for the generalized linear model and characterized by closure
Scale_invariance
Image dataset
at top-5 error rate 25%. The winning team was XRCE by Florent Perronnin, Jorge Sanchez. The system was another linear SVM, running on quantized Fisher vectors
ImageNet
Atom of the element hydrogen
also why the choice of z {\displaystyle z} -axis for the directional quantization of the angular momentum vector is immaterial: an orbital of given ℓ {\displaystyle
Hydrogen_atom
Special mathematical functions defined on the surface of a sphere
Y_{\ell }^{m}(\theta ,\varphi ).} This expansion holds in the sense of mean-square convergence — convergence in L2 of the sphere — which is to say that
Spherical_harmonics
Theorem in classical statistical mechanics
experiment when compared to monatomic gases. The mean kinetic energy also allows the root mean square speed vrms of the gas particles to be calculated:
Equipartition_theorem
Type of signal processing filter
invariance method. For higher orders, digital filters are sensitive to quantization errors, so they are often calculated as cascaded biquad sections, plus one
Butterworth_filter
Type of field appearing in the Lagrangian
From now on we drop the hat and the asterisk. Remember that canonical quantization states ϕ ∼ ( a † + a ) {\displaystyle \phi \sim (a^{\dagger }+a)} . In
Source_field
Specific quantum state of a quantum harmonic oscillator
mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing (see Coherent states in mathematical
Coherent_state
Loss of quantum coherence
mechanics Objective-collapse theory Partial trace Photon polarization Quantization Quantum coherence Quantum Darwinism Quantum entanglement Quantum superposition
Quantum_decoherence
Machine learning technique useful for dimensionality reduction
sum of quadratic bending and stretching energy with the least squares approximation error. The oriented and scalable map (OS-Map) generalises the neighborhood
Self-organizing_map
of a quantum-mechanical system. An improvement of the Bohr–Sommerfeld quantization condition, it allows for the solution of a variety of problems. The Bohr
List of scientific publications by Albert Einstein
List_of_scientific_publications_by_Albert_Einstein
24-dimensional repeating pattern of points
Hadamard code. Quantizers, or analog-to-digital converters, can use lattices to minimise the average root-mean-square error. Most quantizers are based on
Leech_lattice
Grouping a set of objects by similarity
Society: 364–366. doi:10.1093/comjnl/20.4.364. Lloyd, S. (1982). "Least squares quantization in PCM". IEEE Transactions on Information Theory. 28 (2): 129–137
Cluster_analysis
weighted mean when there is a correlation between distances and distance errors for stars in clusters. It is resolved by using an unweighted mean. There
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Classification of Artificial Neural Networks (ANNs)
the output space, and SOM attempts to preserve these. Learning vector quantization (LVQ) can be interpreted as a neural network architecture. Prototypical
Types of artificial neural networks
Types_of_artificial_neural_networks
Ring that is also a vector space or a module
use the term K-algebra to mean an associative algebra over K. A standard first example of a K-algebra is a ring of square matrices over a commutative
Associative_algebra
Set of learning techniques in machine learning
and the optimal weights are found by minimizing the average squared reconstruction error (i.e., difference between an input point and its reconstruction)
Feature_learning
Machine learning model for vision processing
come from a discrete set of "codebook", as in vector quantization. Another encodes the quantized vectors back to image patches. The training objective
Vision_transformer
Representation of the symmetry group of spacetime in special relativity
equation are considered as classical fields prior to (second) quantization. While second quantization and the Lagrangian formalism associated with it is not
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Thermal electromagnetic radiation
was quantized, which is to say that it existed in integer multiples of some quantity. Einstein built on this idea and proposed the quantization of electromagnetic
Black-body_radiation
Particle effect
\alpha _{k}^{2}=I_{4}} . The expectation value is now as if the "root mean square speed" in every direction of space is the speed of light. To add time-dependence
Zitterbewegung
Historical development of physics
physics began in 1900 with Max Planck's discovery of the role of energy quantization in blackbody radiation, a revolutionary idea soon followed by Albert
History_of_physics
Quantum states light can be in
for the variance. (The variance is the mean of the squares of the measuring values minus the square of the mean of the measuring values.) If a mode of
Squeezed_states_of_light
Method of machine learning
Hierarchical temporal memory k-nearest neighbor algorithm Learning vector quantization Perceptron Liang, Juhao; Wang, Ziwei; Ma, Zhuoheng; Li, Jianquan; Zhang
Online_machine_learning
List of concepts in artificial intelligence
theorem provers, and classifiers. k-means clustering A method of vector quantization, originally from signal processing, that aims to partition n observations
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Smooth approximation of one-hot arg max
two modifications: probability scoring, which is an alternative to squared error minimisation, and a normalised exponential (softmax) multi-input generalisation
Softmax_function
Hungarian and American mathematician and physicist (1903–1957)
Doran, Robert S.; Kadison, Richard V., eds. (2004). Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John
John_von_Neumann
Theory of gravitation as curved spacetime
enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime
General_relativity
Creation of hardware designs from software code
additional information is needed on what is an acceptable Mean-Square Error or Bit-Error Rate etc. For example, if the designer starts with an FIR filter
High-level_synthesis
Pictorial representation of the behavior of subatomic particles
Feynman to discover. He discovered it after a long process of trial and error, since he lacked a proper theory of Grassmann integration. The rule follows
Feynman_diagram
Technique for the generative modeling of a continuous probability distribution
{\displaystyle {\mathcal {N}}(\mu ,\Sigma )} is the normal distribution with mean μ {\displaystyle \mu } and variance Σ {\displaystyle \Sigma } , and N ( x
Diffusion_model
Nearest integers from a number
value forms a very basic type of quantizer – a uniform one. A typical (mid-tread) uniform quantizer with a quantization step size equal to some value Δ
Floor_and_ceiling_functions
System used to generate stable voltages, that may be used to define a volt
used for any other measurement. The standard error resulting from sources 3–8 is just the root mean square (RMS) value of the set of short circuit measurements
Josephson_voltage_standard
Subatomic particle with positive charge
distribution, which decays approximately exponentially, with a root mean square charge radius of about 0.8 fm. Protons and neutrons are both nucleons
Proton
Algorithms for matrix decomposition
When L1 regularization (akin to Lasso) is added to NMF with the mean squared error cost function, the resulting problem may be called non-negative sparse
Non-negative matrix factorization
Non-negative_matrix_factorization
Babylonian tablet uses 25⁄8 = 3.125 as an approximation for π, which has an error of 0.5%. 1550 BC: The Rhind Mathematical Papyrus (a copy of an older Middle
Timeline of scientific discoveries
Timeline_of_scientific_discoveries
Theory of rapid universe expansion
Each Fourier mode is normally distributed (usually called Gaussian) with mean zero. Different Fourier components are uncorrelated. The variance of a mode
Cosmic_inflation
Interdisciplinary field
refine its shape according to the image data while minimizing integral error measures, like the active contour model and its variations. Interactive
Medical_image_computing
Albert Einstein's hypothetical situations to argue scientific points
Einstein could calculate the mean square energy fluctuation of the black-body radiation. He found the root mean square energy fluctuation ⟨ ϵ 2 ⟩ {\displaystyle
Einstein's thought experiments
Einstein's_thought_experiments
Method in physics
v e f f {\displaystyle v_{\mathrm {eff} }} is the square root of the harmonic mean of the squares of velocities. By assuming the two transverse polarizations
Debye_model
Infinite series summing alternating 1 and -1 terms
a result of the geometric series formula. Ideally, by searching for the error in reasoning and by investigating the formula for various common ratios
Grandi's_series
Measure of temperature relative to absolute zero
temperature scale (water's boiling point) would be calibrated at the mean barometric pressure at mean sea level. Coincident with the death of Anders Celsius in 1744
Thermodynamic_temperature
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR
MEAN SQUARE-QUANTIZATION-ERROR