Sentence examples for weaker regularization from inspiring English sources

Thus, we obtain additional stronger regularization on the uniform and weaker regularization on the oscillatory patches, which significantly improves resulting image quality.

Although the number of estimated parameters is still greater than the number of observations (G) and, therefore, there still remains a continuum of solutions to equation (2) that have zero error, the large reduction in parameter number allows us to apply a weaker regularization to c n and still avoid over-fitting.

However, it is not clear that there is a weak limit as the regularization is decreased.

The effect of the regularization is weak for, but starts to be significant for and is large for.

Here, we show the well-posedness of the method and derive convergence rates both for convex and non-convex regularization under rather weak conditions.

However, due to the use of a linear regularization, their stability is weaker than that of the commonly used von Schroeter et al.'s deconvolution algorithm in which a nonlinear regularization is used; the linear regularization can make the deconvolution algorithms less tolerant to data errors.

In Section 2, we introduce the function spaces of Orlicz-Sobolev type, give the definition of weak solution to the problem and prove the existence of weak solutions with a method of regularization and the uniqueness of solutions by arguing by contradiction.

Next, the uniqueness of a weak solution is obtained by using the well-known regularization procedure due to Lions.

Rockafellar's [3] proved the weak convergence of his algorithm (1.3) provided that the regularization sequence remains bounded away from zero and the error sequence satisfies the condition.

where J r A = ( I + r A ) − 1, ∀r > 0 is the resolvent of A in a Hilbert space H. Rockafellar [1] proved the weak convergence of the algorithm (1.2) provided that the regularization sequence {c n } remains bounded away from zero, and that the error sequence {e n } satisfies the condition ∑ n = 0 ∞ ∥ e n ∥ < ∞.

He derived a weak convergence result, which shows that for suitable choices of iterative parameters (including the regularization), the sequence of iterative solutions can converge weakly to an exact solution of the SFP.