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In particular, it has been shown that with exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy the RIP with number of measurements nearly linear in the sparsity level. [5] The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices. [6]
The regularization parameter plays a critical role in the denoising process. When =, there is no smoothing and the result is the same as minimizing the sum of squares.As , however, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal.
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.
(This is a 205-page document in .pdf form – the function is defined on p. 178.) M. J. Oreglia, A Study of the Reactions psi prime --> gamma gamma psi, Ph.D. Thesis , SLAC-R-236 (1980), Appendix D. T. Skwarnicki, A study of the radiative CASCADE transitions between the Upsilon-Prime and Upsilon resonances, Ph.D Thesis , DESY F31-86-02(1986 ...
Shape of the impulse response of a typical Gaussian filter. In electronics and signal processing, mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would have infinite impulse response).
The product of two Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the sum of the original variances: = +. The product of two Gaussian probability density functions (PDFs), though, is not in general a Gaussian PDF.
Rössler attractor reconstructed by Takens' theorem, using different delay lengths. Orbits around the attractor have a period between 5.2 and 6.2. In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of that system.