Utilizing the wavelet transform’s structure in compressed sensing

Abstract

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.

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Correspondence to Nicholas Dwork.

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ND would like to thank the Quantitative Biosciences Institute at UCSF and the American Heart Association as funding sources for this work. ND is supported by a Postdoctoral Fellowship of the American Heart Association. ND and PL have been supported by the National Institute of Health’s Grant No. NIH R01 HL136965.

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Dwork, N., O’Connor, D., Baron, C.A. et al. Utilizing the wavelet transform’s structure in compressed sensing. SIViP (2021). https://doi.org/10.1007/s11760-021-01872-y

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Keywords

  • Compressed sensing
  • Compressive sampling
  • Wavelet
  • Basis pursuit
  • MRI