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The procedure of principal component analysis (PCA) is presented which is used as transformation basis to sparsify the signals.
From the recovery algorithm of CS, it can be shown obviously that the appropriate sparse transformation basis ψ can improve recovery precision and reduce the computations.
Where s ¯ denotes the mean vector of S i, y re, y im denote the low-dimensional measurements, P re, P im represent the orthonormal transformation basis constructed based on Equation (7), θ i re and θ i im are the sparse coefficients.
Known the observed vector y and the measurement matrix Φ, sparse transformation basis ψ, the recovery of the unknown signal x could be achieved by searching for the l 0 -sparsest representation that agrees with the measurements [14]: θ ⌢ = arg min θ 0 (5).
According to the above research achievements in SAR raw data compressing based on CS theory, we can see that the SAR imagery data usually have poor sparsity feature and looking for suitable sparse transformation basis for SAR images is extremely significant.
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For adaptation, instead of a normal fMLLR transformation, the basis fMLLR [20] is used.
For practical applications, we provide a novel history matching workflow with a grid connectivity-based transformation (GCT) basis coefficients as parameters for calibration using the gradient-free evolutionary optimization algorithms.
The boundary layer governing equations of PDES are transformed into highly nonlinear coupled ODES and the approximate solutions are derived by the new proposed analytical technique the differential transformation and basis functions method (DTM-BF) on unbounded domains.
The first approach is the basis transformation, for the transformation matrix between Bernstein polynomial basis and Legendre polynomial basis [4], between Bernstein polynomial basis and Chebyshev polynomial basis [5], and between Bernstein polynomial basis and Jacobi polynomial basis [6].
This is accomplished by applying correspondence analysis and transforming the data by basis transformation, so that the principal axis are decreasingly ordered according to their information content.
This method, termed basis transformation, can be seen as a speaker similarity scheme.
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