The chapter includes convolution, correlation, window functions, and a generalized category of norms, Lp-norm, which is used for scaling of data as well as for noise and error estimation.
Based on VFxlogLMP algorithm, we proposed a continuous lp-norm algorithm with logarithmic cost (VFxlogCLMP), which does not need the parameter selection and thresholds estimation.
Then, as main application of these estimates, we obtain a sharp Lp-norm estimate for the Bergman projection, which refines a result of K. Zhu as well as gives a negative answer to a question raised by M. Dostanić.
Specifically, the normalized hybrid image quality metric (NHIQM) and a perceptual relevance weighted Lp-norm are designed, based on the observation that the HVS is trained to extract structural information from the viewing area.
It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the Lp-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero.
Comparing MKL with Lp-norm(p≥2), SMKL obtains a sparse solution by a pre-selection procedure.
As a corollary we show that for a compact abelian group G, and a circle group T for A=Lp(T), 1<p<∞, the Lp-norm is the only one that makes all translations continuous, while for A=C(G), A=L∞(G), or A=L1(G) there are other norms with that property.
We say that a closed subspace H of the space Lp= Lp[0,1], 1⩽p<∞, is a Λ(p -space if, in H, convergence in Lp -spaces equifalent to convergence in measure.
In the paper [ 28], we proposed a weighted iterative shrinkage/thresholding algorithm (WISTA) to solve the lp-norm minimization problem (5) (0 < p < 1).
A generalized H∞-norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived.
This allows a generalized p-norm.
