English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Motivated by a class of nonlinear imaging inverse problems, for instance,multispectral computed tomography (MSCT), this paper studies the convergencetheory of the nonlinear Kaczmarz method (NKM) for solving the system ofnonlinear equations with component-wise convex mapping, namely, the functioncorresponding to each equation being convex. However, such kind of nonlinearmapping may not satisfy the commonly used component-wise tangential conecondition (TCC). For this purpose, we propose a novel condition named relativegradient discrepancy condition (RGDC), and make use of it to prove theconvergence and even the convergence rate of the NKM with several general indexselection strategies, where these strategies include cyclic strategy andmaximum residual strategy. Particularly, we investigate the application of theNKM for solving nonlinear systems in MSCT image reconstruction. We prove thatthe nonlinear mapping in this context fulfills the proposed RGDC rather thanthe component-wise TCC, and provide a global convergence of the NKM based onthe previously obtained results. Numerical experiments further illustrate thenumerical convergence of the NKM for MSCT image reconstruction.

Convergence Analysis of Nonlinear Kaczmarz Method for Systems of Nonlinear Equations with Component-wise Convex Mapping