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multidimensional signal processing is a subset of signal processing (multidimensional signal processing). Nonlinear multi-dimensional systems can be used
Non-linear multi-dimensional signal processing
Non-linear_multi-dimensional_signal_processing
function. Audio signal processing Image processing Towed array sonar X-ray computed tomography Non-linear multi-dimensional signal processing Fast Algorithms
Multidimensional signal processing
Multidimensional_signal_processing
Mathematical signal manipulation by computers
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide
Digital_signal_processing
Process of mapping a continuous set to a countable set
In mathematics and digital signal processing, quantization is the process of mapping input values from a large set (often a continuous set) to output values
Quantization (signal processing)
Quantization_(signal_processing)
Topics referred to by the same term
Non-linear multi-dimensional signal processing (NMSP) Non-Linear (album), 2004 debut studio album by South Korean indie rock band Mot Non-linear editing
Nonlinearity_(disambiguation)
Algorithms for matrix decomposition
data imputation, chemometrics, audio signal processing, recommender systems, and bioinformatics. In chemometrics non-negative matrix factorization has a
Non-negative matrix factorization
Non-negative_matrix_factorization
Method of data analysis
linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data are linearly
Principal_component_analysis
Function in discrete mathematics
digital signal processing, the input is often a sampled quantity or signal that varies over time, such as the pressure of a sound wave, a radio signal, or
Discrete_Fourier_transform
Separation of a set of source signals from a set of mixed signals
source signals or the mixing process. It is most commonly applied in digital signal processing and involves the analysis of mixtures of signals; the objective
Signal_separation
Difficulties arising when analyzing data with many aspects ("dimensions")
high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression
Curse_of_dimensionality
Process of calculating the causal factors that produced a set of observations
signal processing, medical imaging, computer vision, geophysics, oceanography, meteorology, astronomy, remote sensing, natural language processing, machine
Inverse_problem
isosurface from a three-dimensional scalar field (sometimes called voxels) Marching squares: generates contour lines for a two-dimensional scalar field Marching
List_of_algorithms
Systematic collection of geophysical data for spatial studies
these signals as well. Hence this article also discusses multi-dimensional signal processing techniques. Geophysical surveys can involve a wide range
Geophysical_survey
Subset of artificial intelligence
introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space. Multivariate linear regression
Machine_learning
Type of feedforward neural network
with a linear activation function. For binary classification (predicting yes/no), it uses a single neuron with a sigmoid activation. For multi-class classification
Multilayer_perceptron
Fitting an approximating function to data
simple series of data points (rather than a multi-dimensional image), the convolution kernel is a one-dimensional vector. One of the most common algorithms
Smoothing
Pattern defining an infinite sequence of numbers
or one-dimensional recurrence relations are about sequences (i.e. functions defined on one-dimensional grids). Multi-variable or n-dimensional recurrence
Recurrence_relation
Type of resistor, usually with three terminals
types of non-contact potentiometers can probably be built), and then an electronic circuit does the signal processing to provide an output signal that can
Potentiometer
Mathematical concept
optimization Leximin order Multiple-criteria decision-making Multi-objective linear programming Multi-disciplinary design optimization Pareto efficiency Utility
Multi-objective_optimization
Algorithm for modelling sequential data
window with other (unmasked) tokens via a parallel multi-head attention mechanism, allowing the signal for key tokens to be amplified and less important
Transformer_(deep_learning)
Least variables needed to represent data
concept has widespread applications in geometry, dynamical systems, signal processing, statistics, and other fields. Due to its widespread applications
Intrinsic_dimension
Branch of machine learning
networks that contain many layers of non-linear hidden units and a very large output layer. By 2019, graphics processing units (GPUs), often with AI-specific
Deep_learning
Concept in applied mathematics
In applied mathematics, the non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier
Non-uniform discrete Fourier transform
Non-uniform_discrete_Fourier_transform
Particular representation of a signal
In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary
Analytic_signal
Filters used in signal processing that are optimal in some sense
response is matched to input pulse signals. Two-dimensional matched filters are commonly used in image processing, e.g., to improve the SNR of X-ray observations
Matched_filter
Object detection system using radio waves
Pulse-Doppler signal processing, moving target detection processors, correlation with secondary surveillance radar targets, space-time adaptive processing, and
Radar
measurement data, signal generation, windowing, filter functions, signal processing, linear algebra, array and complex operations, curve fitting and statistics
List_of_numerical_libraries
Specialized electronic circuit that accelerates graphics
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being
Graphics_processing_unit
possible to extract two-dimensional spectra as a function of excitation and detection frequencies. Although third-order two-dimensional spectroscopy is historically
Two-dimensional electronic spectroscopy
Two-dimensional_electronic_spectroscopy
Algorithm that estimates unknowns from a series of measurements over time
Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion
Kalman_filter
which can be one-dimensional, two-dimensional or multidimensional. In most cases, the variable of one-dimensional analog signals are time. After the
Two-dimensional_filter
Signal processing technique for sensor arrays
Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved
Beamforming
Concept in machine learning
often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core
Tensor_(machine_learning)
Use of a GPU for computations typically assigned to CPUs
General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit (GPU), which typically handles
General-purpose computing on graphics processing units
General-purpose_computing_on_graphics_processing_units
Transform in numerical harmonic analysis
requires access to the entire signal at once. It also applies to the multi-scale transform and also to the multi-dimensional transforms (e.g., 2-D DWT).
Discrete_wavelet_transform
Type of artificial neural network
recurrent neural network, in which loops allow information from later processing stages to feed back to earlier stages. Feedforward multiplication is essential
Feedforward_neural_network
Correlation of a signal with a time-shifted copy of itself, as a function of shift
of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These
Autocorrelation
Technique for the generative modeling of a continuous probability distribution
it by other models. Upscaling can be done by GAN, Transformer, or signal processing methods like Lanczos resampling. Diffusion models themselves can be
Diffusion_model
Mathematical function
describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian
Gaussian_function
Reconstruction of quantum states based on measurements
solution then lies on the boundary of the n-dimensional Bloch sphere. This can be seen as related to linear inversion giving states which lie outside the
Quantum_tomography
Canadian engineer (1941–2014)
foundations of two-dimensional and multi-dimensional digital filtering. These techniques are widely used in image and video processing. His early contributions
Anastasios_Venetsanopoulos
Statistical model
distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are useful in statistical
Gaussian_process
Set of learning techniques in machine learning
learning is often to discover low-dimensional features that capture some structure underlying the high-dimensional input data. When the feature learning
Representation_learning
reflects this. Early arrays targeted digital signal processing, multimedia, and image and video processing, where the same operations are applied to streams
Coarse-grained reconfigurable array
Coarse-grained_reconfigurable_array
Function for integral Fourier-like transform
Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of middle C
Wavelet
Central computer component that executes instructions
Accelerated Processing Unit Complex instruction set computer Computer bus Computer engineering CPU core voltage CPU socket Data processing unit Digital signal processor
Central_processing_unit
Unit of information in a quantum computer
can be expressed as a vector within the 𝑑-dimensional Hilbert space H𝑑, and it can be written as a linear combination |𝜓⟩=𝛼0· |0⟩+𝛼1· |1⟩+...+𝛼𝑑−1
Qudit
Programming paradigm in which many processes are executed simultaneously
have a near-linear speedup for small numbers of processing elements, which flattens out into a constant value for large numbers of processing elements.
Parallel_computing
Sequence of data points over time
non-stationarity) Bivariate linear measures Maximum linear cross-correlation Linear Coherence (signal processing) Bivariate non-linear measures Non-linear
Time_series
Computational model used in machine learning
is computed by some non-linear function of the totality of its inputs, called the activation function. The strength of the signal at each connection is
Neural network (machine learning)
Neural_network_(machine_learning)
Machine learning technique
"Committee Machines". Handbook of Neural Network Signal Processing. Electrical Engineering & Applied Signal Processing Series. Vol. 5. doi:10.1201/9781420038613
Mixture_of_experts
Algorithm to smooth data points
increase the precision of the data without distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets
Savitzky–Golay_filter
In signal processing it is useful to simultaneously analyze the space and frequency characteristics of a signal. While the Fourier transform gives the
Log_Gabor_filter
programmable spectral filter. From signal processing point of view, the AOPDF corresponds to a time-variant passive linear transversal filter with a programmable
Acousto-optic programmable dispersive filter
Acousto-optic_programmable_dispersive_filter
Type of feedforward neural network
2x2 dimension. This implies that the input is drastically downsampled, reducing processing cost. Greater pooling reduces the dimension of the signal, and
Convolutional_neural_network
Method of encoding digital data on multiple carrier frequencies
on Signal Processing, Oct. 2012) that applying the MMSE linear receiver to each vector subchannel (1), it achieves multipath diversity and/or signal space
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Real-valued number of spatial dimensions
sets); 1 for sets describing lines (1-dimensional sets having length only); 2 for sets describing surfaces (2-dimensional sets having length and width); and
Fractal_dimension
Tool for digital signal processing
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one
Filter_bank
Linear filter used for texture analysis
In image processing, a Gabor filter, named after Dennis Gabor, who first proposed it as a 1D filter, is a linear filter used for texture analysis, which
Gabor_filter
Branch of engineering and mathematics
and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop. In the case of linear feedback
Control_theory
an inhomogeneous Poisson process. The linear filtering stage performs dimensionality reduction, reducing the high-dimensional spatio-temporal stimulus
Linear-nonlinear-Poisson cascade model
Linear-nonlinear-Poisson_cascade_model
Signal processing computational method
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents.
Independent component analysis
Independent_component_analysis
Form of radar used to create images of landscapes
radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes. SAR uses
Synthetic-aperture_radar
Nonlinear two-terminal fundamental circuit element
A memristor (/ˈmɛmrɪstər/; a portmanteau of memory resistor) is a non-linear two-terminal electrical component relating electric charge and magnetic flux
Memristor
Navigation and surveillance technique
and m is the number of signals received (thus, TOFs measured), it is required that m ≥ d + 1 {\displaystyle m\geq d+1} . Processing is usually required to
Pseudo-range_multilateration
Technique used in signal processing and data compression
Technically, computing a two-, three- (or -multi) dimensional DCT by sequences of one-dimensional DCTs along each dimension is known as a row-column algorithm
Discrete_cosine_transform
Machine learning paradigm
lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves
Self-supervised_learning
Mathematical transform that expresses a function of time as a function of frequency
with divergent or critical elements. Two particular examples from linear signal processing are the construction of allpass filter networks from critical comb
Fourier_transform
Field of machine learning
approximation methods are used. Linear function approximation starts with a mapping ϕ {\displaystyle \phi } that assigns a finite-dimensional vector to each state-action
Reinforcement_learning
Mathematical technique used in data compression and analysis
frequency of the basis function. Based on the uncertainty principle of signal processing, Δ t Δ ω ≥ 1 2 {\displaystyle \Delta t\Delta \omega \geq {\frac {1}{2}}}
Wavelet_transform
Devices that measure magnetic field strength using the Hall effect
voltage for a convenient analog signal output proportional to the magnetic field component. In some cases, the linear circuit may cancel the offset voltage
Hall-effect_sensor
Automated recognition of patterns and regularities in data
business use. Pattern recognition focuses more on the signal and also takes acquisition and signal processing into consideration. It originated in engineering
Pattern_recognition
Computer that uses photons or light waves
waves, such as light, than for the electronic signals in a conventional computer. This may require processing elements with more power and larger dimensions
Optical_computing
optimization: Rosenbrock function — two-dimensional function with a banana-shaped valley Himmelblau's function — two-dimensional with four local minima, defined
List of numerical analysis topics
List_of_numerical_analysis_topics
Algorithmic processing of digitally-represented images
image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital
Digital_image_processing
Partitioning a digital image into segments
(reconstructed) image. New methods suggest the use of multi-dimensional, fuzzy rule-based, non-linear thresholds. In these approaches, the decision regarding
Image_segmentation
Use of multiple antennas in radio
antennas at both the transmitter and receiver, along with associated signal processing, to deliver data rate speedups roughly proportional to the number
MIMO
Touchscreen interactions using multiple fingers
2017-02-24 Lee, SK; Buxton, William; Smith, K. C. (1985-01-01). "A multi-touch three dimensional touch-sensitive tablet". Proceedings of the SIGCHI conference
Multi-touch
Statistical distribution for dependence between random variables
1]^{d}\rightarrow [0,1]} is a d-dimensional copula if C is a joint cumulative distribution function of a d-dimensional random vector on the unit cube [
Copula_(statistics)
Research field that lies at the intersection of machine learning and computer security
properties of adversarially-trained linear regression. Thirty-seventh Conference on Neural Information Processing Systems. Tsipras, Dimitris; Santurkar
Adversarial_machine_learning
Feedback controller
and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop. In the case of linear feedback
Closed-loop_controller
Micro-electronic component
digital signals for mathematical processing. Digital signal processor (DSP) cores are often included on SoCs. They perform signal processing operations
System_on_a_chip
Artificial neural network node function
wavelet shrinkage for non-parametric estimation" (PDF), 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3265–3268, doi:10
Activation_function
MRI procedure that measures brain activity by detecting associated changes in blood flow
replication performed by David T Field has now demonstrated—using modern signal processing techniques unavailable to Mosso—that a balance apparatus of this type
Functional magnetic resonance imaging
Functional_magnetic_resonance_imaging
Integrated circuit composed of several vertically stacked chips
Development History of Three-Dimensional Integration Technology" (PDF). Three-Dimensional Integration of Semiconductors: Processing, Materials, and Applications
Three-dimensional integrated circuit
Three-dimensional_integrated_circuit
Representation learning method
or signal recovery. In compressed sensing, a high-dimensional signal can be recovered with only a few linear measurements, provided that the signal is
Sparse_dictionary_learning
Area of research in signal processing
Array processing is a wide area of research in the field of signal processing that extends from the simplest form of 1 dimensional line arrays to 2 and
Array_processing
Vector quantization algorithm minimizing the sum of squared deviations
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each
K-means_clustering
Recurrent neural network architecture
IEEE International Conference on Image Processing (ICIP). 25th IEEE International Conference on Image Processing (ICIP). pp. 918–922. doi:10.1109/icip
Long_short-term_memory
Neural network that learns efficient data encoding in an unsupervised manner
representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine
Autoencoder
Mathematical algorithm
methods when applied to such problems as training linear support vector machines (see LIBLINEAR) and non-negative matrix factorization. They are attractive
Coordinate_descent
Type of image noise
and non-adaptive filters on the signal processing (where adaptive filters adapt their weightings across the image to the speckle level, and non-adaptive
Speckle_(interference)
Integral expressing the amount of overlap of one function as it is shifted over another
analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.[citation needed] Computing
Convolution
Class of artificial neural network
the dominant architecture for many sequence-processing tasks, particularly in natural language processing, due to their superior handling of long-range
Recurrent_neural_network
Solving multiple machine learning tasks at the same time
Chai, K. M., & Williams, C. (2008). Multi-task Gaussian process prediction. Advances in neural information processing systems (pp. 153-160). Ong, Y. S.
Multi-task_learning
Group of sensors used to increase gain or dimensionality over a single sensor
require more complex signal processing techniques for parameter estimation. In uniform linear array (ULA) the phase of the incoming signal ω τ {\displaystyle
Sensor_array
Theorem in mathematics
{F}}^{-1}\{U\cdot V\}.} (Eq.1b) The theorem also generally applies to multi-dimensional functions. This theorem also holds for the Laplace transform, the
Convolution_theorem
Spectroscopic technique based on change of nuclear spin state
sample. In multi-dimensional nuclear magnetic resonance spectroscopy, there are at least two pulses: one leads to the directly detected signal and the others
Nuclear_magnetic_resonance
Algorithm for measuring similarity between temporal sequences
"warped" non-linearly in the time dimension to determine a measure of their similarity independent of certain non-linear variations in the time dimension. This
Dynamic_time_warping
Automatic conversion of spoken language into text
on Packet Networks: Part II of Linear Predictive Coding and the Internet Protocol" (PDF). Found. Trends Signal Process. 3 (4): 203–303. doi:10.1561/2000000036
Speech_recognition
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