نتایج جستجو برای: tikhonov regularization
تعداد نتایج: 21274 فیلتر نتایج به سال:
We consider a “local” Tikhonov regularization method for ill-posed Volterra problems. In addition to leading to efficient numerical schemes for inverse problems of this type, a feature of the method is that one may impose varying amounts of local smoothness on the solution, i.e., more regularization may be applied in some regions of the solution’s domain, and less in others. Here we present pro...
In this paper, we present a novel approach to imaging sparse and focal neural current sources from MEG (magnetoencephalography) data. Using the framework of Tikhonov regularization theory, we introduce a new stabilizer that uses the concept of controlled support to incorporate a priori assumptions about the area occupied by focal sources. The paper discusses the underlying Tikhonov theory and i...
We consider solution of linear ill-posed problem Au = f by Tikhonov method and by Lavrentiev method. For increasing the qualification and accuracy of these methods we use extrapolation, taking for the approximate solution linear combination of n ≥ 2 approximations of Tikhonov or Lavrentiev methods with different parameters and with proper coefficients. If the solution u∗ belongs to R((A A)) and...
We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly relat...
Abstract This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such we consider regularizers consisting two terms that must balanced. Namely, a Tikhonov term guarantees the smoothness solution component, while total-variation (TV) regularizer promotes blockiness non-smooth component. A ...
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