Sparsity fine tuning in wavelet domain with application to compressive image reconstruction

Area of Science:

• Signal Processing
• Image Reconstruction
• Statistical Modeling

Background:

• Wavelet transforms are standard for sparse signal representation in compressive sensing.
• Existing methods often assume zero-mean high-frequency wavelet coefficients, which can limit sparsity.

Purpose of the Study:

• To develop a novel statistical context modeling approach to increase wavelet image representation sparsity.
• To improve the performance of compressive image reconstruction (CIR) algorithms.

Main Methods:

• Proposed a statistical context modeling technique to address non-zero mean distributions of high-frequency wavelet coefficients.
• Developed an efficient algorithm for compressive image recovery (CIR) utilizing the refined models.

Main Results:

• Demonstrated that conditioning on local image structures reveals non-zero means in high-frequency wavelet coefficients.
• Removing this bias significantly increases the sparsity of wavelet image representations.
• The new unbiased probability models enhanced existing wavelet-based CIR methods.

Conclusions:

• The proposed method effectively increases wavelet image sparsity by modeling coefficient distributions.
• The refined models lead to significant improvements in both PSNR and visual quality for CIR.
• The novel CIR method outperforms existing approaches on simulated and real CS image data.