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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]
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Gaussian basis sets are used in Turbomole. The functionality of the program concentrates extensively on the electronic structure methods with effective cost-performance characteristics such as density functional theory , [ 3 ] second–order Møller-Plesset [ 4 ] [ 5 ] and coupled cluster theory .
It is sometimes referred to as "4D Gaussian splatting"; however, this naming convention implies the use of 4D Gaussian primitives (parameterized by a 4×4 mean and a 4×4 covariance matrix). Most work in this area still employs 3D Gaussian primitives, applying temporal constraints as an extra parameter of optimization.
Tomographic reconstruction: Projection, Back projection and Filtered back projection. Tomographic 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.
(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 ...
T-coloring-- T distribution-- T-duality-- T-group (mathematics)-- T-norm-- T-norm fuzzy logics-- T puzzle-- T-schema-- T-spline-- T-square (fractal)-- T-statistic-- T-structure-- T-symmetry-- T-table-- T-theory-- T(1) theorem-- T.C. Mits-- T1 process-- T1 space-- Table of bases-- Table of Clebsch–Gordan coefficients-- Table of congruences-- Table of costs of operations in elliptic curves ...
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.