SPECT reconstruction using DCT-induced tight framelet regularization

Jiahan Zhang, Si Li, Yuesheng Xu, C. R. Schmidtlein, Edward D. Lipson, David H. Feiglin, Andrzej Krol

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the 1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the 1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the 1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.

Original languageEnglish (US)
Title of host publicationProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISBN (Print)9781628415025
StatePublished - 2015
EventMedical Imaging 2015: Physics of Medical Imaging - Orlando, United States
Duration: Feb 22 2015Feb 25 2015


OtherMedical Imaging 2015: Physics of Medical Imaging
CountryUnited States



  • DCT
  • Framelet
  • Image reconstruction
  • Noise reduction
  • Re gularization

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Radiology Nuclear Medicine and imaging

Cite this

Zhang, J., Li, S., Xu, Y., Schmidtlein, C. R., Lipson, E. D., Feiglin, D. H., & Krol, A. (2015). SPECT reconstruction using DCT-induced tight framelet regularization. In Progress in Biomedical Optics and Imaging - Proceedings of SPIE (Vol. 9412). [94123H] SPIE. https://doi.org/10.1117/12.2082118