Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging

• Published in: IEEE transactions on medical imaging Vol. 22; no. 3; pp. 332 - 350
• Main Authors: Willett, R.M., Nowak, R.D.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-03-2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Biomedical imaging; Distributed computing; Humans; Image decomposition; Image denoising; Image Enhancement - instrumentation; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image reconstruction; Imaging, Three-Dimensional - methods; Medical imaging; Microscopy; Microscopy, Confocal - instrumentation; Microscopy, Confocal - methods; Pattern Recognition, Automated; Phantoms, Imaging; Photons; Piecewise linear approximation; Piecewise linear techniques; Reconstruction algorithms; Scattering, Radiation; Signal Processing, Computer-Assisted; Single photon emission computed tomography; Stochastic Processes; Studies; Tomography, Emission-Computed - instrumentation; Tomography, Emission-Computed - methods; Tomography, Emission-Computed, Single-Photon - instrumentation; Tomography, Emission-Computed, Single-Photon - methods
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2003.809622

The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional wavelet-based methods, are both well suited to photon-limited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized functions at various scales, locations, and orientations that produce piecewise linear image approximations, and a new multiscale image decomposition based on these functions. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in certain Holder classes, it is shown that the error of m-term platelet approximations can decay significantly faster than that of m-term approximations in terms of sinusoids, wavelets, or wedgelets. This suggests that platelets may outperform existing techniques for image denoising and reconstruction. Fast, platelet-based, maximum penalized likelihood methods for photon-limited image denoising, deblurring and tomographic reconstruction problems are developed. Because platelet decompositions of Poisson distributed images are tractable and computationally efficient, existing image reconstruction methods based on expectation-maximization type algorithms can be easily enhanced with platelet techniques. Experimental results suggest that platelet-based methods can outperform standard reconstruction methods currently in use in confocal microscopy, image restoration, and emission tomography.