SignalIn signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.
Tomographic reconstructionTomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner.
Finite volume methodThe finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.
K-nearest neighbors algorithmIn statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression: In k-NN classification, the output is a class membership.
Total variation denoisingIn signal processing, particularly , total variation denoising, also known as total variation regularization or total variation filtering, is a noise removal process (filter). It is based on the principle that signals with excessive and possibly spurious detail have high total variation, that is, the integral of the absolute is high. According to this principle, reducing the total variation of the signal—subject to it being a close match to the original signal—removes unwanted detail whilst preserving important details such as .
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Sampling (signal processing)In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.
Total variationIn mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure. For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x), for x ∈ [a, b]. Functions whose total variation is finite are called functions of bounded variation.
Analog signalAn analog signal is any continuous-time signal representing some other quantity, i.e., analogous to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies continuously with the pressure of the sound waves. In contrast, a digital signal represents the original time-varying quantity as a sampled sequence of quantized values. Digital sampling imposes some bandwidth and dynamic range constraints on the representation and adds quantization error.
