A cartoon-texture approach for JPEG/JPEG 2000 decompression based on TGV and shearlet transform.

Area of Science:

• Image Processing
• Computer Vision
• Applied Mathematics

Background:

• JPEG and JPEG 2000 compression introduce artifacts that degrade image quality.
• Existing variational methods struggle with preserving fine textures during decompression.
• The need for artifact-free image reconstruction with enhanced texture preservation is critical.

Purpose of the Study:

• To propose a novel artifact-free variational model for JPEG/JPEG 2000 decompression.
• To improve the reconstruction of piecewise smooth images with structured textures.
• To enhance the quality of decompressed images through advanced regularization techniques.

Main Methods:

• Developed a cartoon-texture decomposition scheme for image analysis.
• Employed infimal convolution regularization with Total Generalized Variation (TGV) and shearlet transform.
• Incorporated an L2 cost functional and utilized the proximal Primal-Dual method for efficient solving.

Main Results:

• The proposed model successfully reconstructs images with piecewise smooth regions and structured textures.
• Shearlet transform effectively captures texture singularities and orientations.
• Numerical experiments demonstrate competitive performance against the Trainable Nonlinear Reaction Diffusion (TNRD) method in texture preservation.

Conclusions:

• The new variational model offers superior artifact-free decompression for JPEG/JPEG 2000 images.
• It significantly outperforms traditional TV-based and TGV-based variational methods in image reconstruction quality.
• The model provides a robust solution for preserving image details and textures.