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<p>Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double phase models. We study the norm and modular of the new space and derive a formula for the modular in terms of the Lebesgue decomposition of the derivative measure and a location dependent recession function. We also show that the modular can be obtained as the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3731_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-limit of uniformly convex approximating energies.</p>

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Bounded variation spaces with generalized Orlicz growth related to image denoising

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月7日

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  • Michela Eleuteri,
  • Petteri Harjulehto,
  • Peter Hästö

摘要

Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double phase models. We study the norm and modular of the new space and derive a formula for the modular in terms of the Lebesgue decomposition of the derivative measure and a location dependent recession function. We also show that the modular can be obtained as the \(\Gamma \) Γ -limit of uniformly convex approximating energies.