Image Recovery via Transform Learning and Low-Rank Modeling: The Power of Complementary Regularizers.

Area of Science:

• Image Processing
• Signal Modeling
• Computer Vision

Background:

• Adaptive sparse and low-rank signal modeling are useful in image/video processing.
• Patch-based methods exploit local sparsity; others use grouped patch low-rankness for non-local structures.
• Existing methods using only sparsity or low-rankness limit image reconstruction performance.

Purpose of the Study:

• Propose a simultaneous sparsity and low-rank model (STROLLR) for improved natural image representation.
• Develop an image restoration framework leveraging both local and non-local image properties.
• Utilize transform learning with joint low-rank regularization for efficient and effective image restoration.

Main Methods:

• Developed the STROLLR model integrating simultaneous sparsity and low-rank priors.
• Implemented a transform learning scheme for adaptive sparse representation.
• Applied joint low-rank regularization within the image restoration framework.

Main Results:

• The STROLLR model effectively represents natural images by combining local and non-local properties.
• The transform learning approach offers computational efficiency and good performance.
• Demonstrated promising results in image denoising, inpainting, and compressed sensing MRI compared to state-of-the-art methods.

Conclusions:

• The proposed STROLLR framework offers a powerful approach for image restoration.
• Simultaneous sparsity and low-rank modeling, coupled with transform learning, significantly improves image reconstruction.
• The method shows broad applicability and superior performance across diverse imaging applications.