Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods finding the minimizer norm‐based in Banach spaces. One is steepest descent method, whereby iterations directly carried out underlying space, and other one performs dual space. prove strong convergence both methods.

We investigate a method of accelerated Landweber type for the iterative regularization nonlinear ill-posed operator equations in Banach spaces. Based on an auxiliary algorithm with simplified choice step-size parameter we present convergence and stability analysis under consideration. will close our discussion presentation numerical example.

We introduce and discuss an iterative method of modified Landweber type for regularization nonlinear operator equations in Banach spaces. Under smoothness convexity assumptions on the solution space we present convergence stability results. Furthermore, will show that under so-called approximate source conditions rates may be achieved by a proper a-priori choice parameter presented algorithm. illustrate these theoretical results with numerical example.

This paper presents Tikhonov- and iterated soft-shrinkage regularization methods for nonlinear inverse medium scattering problems. Motivated by recent sparsity-promoting reconstruction schemes problems, we assume that the contrast of is supported within a small subdomain known search domain minimize Tikhonov functionals with penalty terms based on Lp-norms. Analytically, this theory Helmholtz equation refractive index in Lp, 1 < p ∞, crucial continuity compactness properties...

Precise measurement of mechanical forces is crucial to efficient micro-manufacturing. The quality such measurements depends heavily on the properties noise inevitably accompanying every process. In micro-range, signal-to-noise ratio tends be very low, and dynamic varies for different frequencies. result, common denoising methods that assume white perform poorly in this setting. paper, a novel, easily implementable method based local statistic measured data’s spectrum proposed. By testing it...

Abstract. In this paper we deal with Besov spaces . We show that generalized forms of the polarization identity hold for wavelet-characterization space norm. particular these are smooth power type and convex

One feasible way to minimize a non-smooth functional is replace it by some smoothed version, which leads surrogate minimization problem that easily treated standard means. A prominent example of such given Tikhonov-type incorporating sparsity-enforcing penalty term. It has received enormous attention in recent years, yet its efficient remains challenging. In this paper we consider general functionals and show, under mild conditions, the stability their minimizer with respect replacement term...

We consider the Tikhonov functional incorporating a ℓp-norm as penalty term. The minimizer of this is investigated in regard to its sensitivity with respect parameter p. To quantify minimizer, we determine derivative underlying idea based on implicit function theorem. show that differentiable p for any 1 < 2. For = 1, exists only under additional assumptions.

The DjVu file format and image compression techniques are widely used in the archival of digital documents. Its key ingredients separation document into fore- background layers a binary switching mask, followed by lossy, transform-based former dictionary-based latter. lossy is based on wavelet decomposition bit truncation, which leads, particular at higher rates, to severe artifacts standard decompression layers. aim this paper break ground for variational files. To aim, we provide an...

Sporadic machine-to-machine communication requires a signaling efficient medium access strategy, which can be achieved by compressed sensing based multi-user detection (CS-MUD). This novel application for Compressed Sensing adapted reconstruction algorithms considering typical communications assumptions. In order to get fast signal reconstruction, we utilize smoothed version of the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub>...

IPscatt is a free, open-source MATLAB toolbox facilitating the solution for time-independent scattering (also known as time-harmonic scattering) in two- and three-dimensional settings. The has three main application cases: simulation of scattered field given transmitter-receiver geometry; generation simulated data well handling real-world from Institute Fresnel; reconstruction contrast several measured, fields. In each case, variety options tailored to needs practitioners provided. For...