Utilizing the wavelet transform's structure in compressed sensing

Compressed sensing has empowered quality image reconstruction with fewer data samples than previously thought possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is commonly used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns using both magnetic resonance and optical images.

Automated summary

In this study, the structure of the Daubechies wavelet transform was utilized to identify an affine transformation that increases sparsity, improving quality image reconstruction through compressed sensing techniques. By modifying the optimization problem and complying with the Basis Pursuit Denoising problem, a lower bound on reconstruction error was theoretically achieved, resulting in higher quality images for the same sampling patterns.