2020/02/29 by Nicholas Dwork, Daniel O’Connor, Daniel O'Connor +5
Computer Science · Engineering · #Advanced Image Fusion Techniques #Affine transformation #Compressed sensing #Discrete wavelet transform #Image and Signal Denoising Methods #Iterative reconstruction #Noise reduction #Pattern recognition (psychology) #Sparse and Compressive Sensing Techniques #Transformation (genetics) #Wavelet #Wavelet transform #eess.IV
paper · pdf · doi:10.1007/s11760-021-01872-y
published as Signal, Image and Video Processing (2021): 1-8
openalex created_date 2020/02/24 · openalex publication_date 2021/03/09 · arxiv created 2021/06/16 · arxiv updated 2021/06/17 · openalex updated_date 2026/08/06
Compressed sensing has empowered quality image reconstruction with fewer data samples than previously though possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is a common sparsifying transformation 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.