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Babel Function
The Babel function (also known as cumulative coherence) measures the maximum total coherence between a fixed atom and a collection of other atoms in a dictionary. The Babel function was conceived of in the context of signals for which there exists a sparse representation consisting of atoms or columns of a redundant dictionary matrix, A. Definition and formulation The Babel function of a dictionary \boldsymbol with normalized columns is a real-valued function that is defined as ::\mu_1(p) = \max_ \ where \boldsymbol_k are the columns (atoms) of the dictionary \boldsymbol . Special case When p=1, the babel function is the mutual coherence. Practical Applications Li and Lin have used the Babel function to aid in creating effective dictionaries for Machine Learning applications. References {{reflist See also * Compressed sensing Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (signal Processing)
In signal processing, the coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input and output. Definition and formulation The coherence (sometimes called magnitude-squared coherence) between two signals x(t) and y(t) is a real-valued function that is defined as: ::C_(f) = \frac where Gxy(f) is the Cross-spectral density between x and y, and Gxx(f) and Gyy(f) the auto spectral density of x and y respectively. The magnitude of the spectral density is denoted as , G, . Given the restrictions noted above (ergodicity, linearity) the coherence function estimates the extent to which y(t) may be predicted from x(t) by an optimum linear least squares function. Values of coherence will always satisfy 0\le C_(f)\le 1. For an ''ideal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atom (sparse Signal Analysis)
An atom is a particle that consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. The atom is the basic particle of the chemical elements, and the chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms are extremely small, typically around 100 picometers across. A human hair is about a million carbon atoms wide. This is smaller than the shortest wavelength of visible light, which means humans cannot see atoms with conventional microscopes. Atoms are so small that accurately predicting their behavior using classical physics is not possible due to quantum effects. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
