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 o...

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Bibliographic Details
Published in:Signal, image and video processing image and video processing, 2021-10, Vol.15 (7), p.1407-1414
Main Authors: Dwork, Nicholas, O’Connor, Daniel, Baron, Corey A., Johnson, Ethan M. I., Kerr, Adam B., Pauly, John M., Larson, Peder E. Z.
Format: Article
Language:English
Subjects:
Affine transformations
Computer Imaging
Computer Science
Image Processing and Computer Vision
Image quality
Image reconstruction
Linear transformations
Lower bounds
Magnetic resonance
Multimedia Information Systems
Optimization
Original Paper
Pattern Recognition and Graphics
Signal,Image and Speech Processing
Vision
Wavelet transforms
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Summary: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.
ISSN:1863-1703
1863-1711
DOI:10.1007/s11760-021-01872-y