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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:33 |
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Conference: Bucharest University Faculty of Physics 2012 Meeting
Section: Biophysics; Medical Physics
Title:
Nyquist violated? No way!
Authors:
R. MUTIHAC
Affiliation:
Department of Physics, University of Bucharest, 077125 ROMANIA
Division of Psychiatry and Neuroscience, Walter Reed Army Institute, Silver Spring, MD 20910, USA
National Institutes of Health, Bethesda, MD 20892, USA
E-mail
radu.mutihac@nih.gov
Keywords:
compressed sensing, wavelet transform, sparse data, magnetic resonance imaging
Abstract:
Compressed Sensing or Compressive Sampling (CS) is an approach to faithfully reconstruct sparse signals from under-sampled measurements acquired below the Shannon-Nyquist rate. CS yields a stricter sampling condition disclosing a sub-Nyquist sampling criterion. Transform-based compression of images is adopted in standards like JPEG or MPEG. Essentially, the strategy consists in applying a sparsifying transform that maps the image content into a vector of sparse coefficients, and subsequently encoding the sparse vector by approximation of the most significant coefficients and discarding the smaller ones. As such, thresholding is a crucial issue in accurate reconstruction of the original image. We employed wavelets and the transformed data were thresholded in the wavelet domain in compliance with the Stein unbiased risk estimator (SURE) proved to be optimal in some sense. The mean squared error (MSE) was used to evaluate the performance of various algorithms.Application of CS is conditioned by: (i)transform sparsity: sparsely represented image in a transform domain (wavelets); (ii)Incoherence of undersampling artifacts: incoherent (noise like) artifacts in the sparsifying transform domain caused by k-space undersampling in linear reconstruction;(iii) Nonlinear reconstruction: reconstructed images by a nonlinear method that enforces both sparsity of the image representation and consistency of the reconstruction with the acquired samples.Magnetic resonance imaging (MRI) has emerged as a non-invasive medical imaging technique, yet limited by relatively slow data acquisition. Any CS protocol for MRI amounts to selecting a subset of frequency domain that can be efficiently sampled and is incoherent with respect to the sparsifying transform. As such, CS is able to make accurate reconstructions from a small subset of k-space, rather than an entire k-space grid. Applying CS to MRI entails significant scan time reductions that are beneficial for patient comfort, large data processing, and effective diagnosis.The success of CS is proven today by the tomosynthesis mammography.
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