In this work, we introduce a novel variational model for decomposing an image into smooth “cartoon” and oscillatory “texture” components. The approach builds on classical total-variation (TV) and G-norm decomposition frameworks: for example, \cite{ROF} proposed a TV model for cartoon denoising, and Meyer \cite{Meyer} introduced G-norm to characterize texture oscillations, which has been studied further by \cite{OSV} defining various approximations to G norm. A key innovation is the Total Symmetric Variation (TSV), a non-local measure of symmetric intensity differences computed via a weighted non-local gradient. TSV is high at region boundaries and low in homogeneous/textured interiors. The proposed energy uses TSV to weight Meyer’s G-norm: the oscillatory penalty is strong in uniform regions and suppressed near edges, ensuring that textures are extracted without blurring contours. The resulting variational model couples a TV-regularized cartoon term with a TSV-weighted G-norm texture term, and the authors prove existence of a minimizer for images with bounded TSV. To solve the nonconvex optimization, we devise a fast operator-splitting (ADMM-like) algorithm, akin to recent splitting methods in image processing \cite{Deng}. Numerical experiments on synthetic and real images, including challenging textured mosaics, demonstrate that the method effectively separates cartoon and texture: sharp edges and shapes are preserved in the cartoon output, while fine textures are isolated in the texture output.