Abstract
The sparsity regularization approach, which assumes that the image of interest is likely to have sparse representation in some transform domain, has been an active research area in image processing and medical image reconstruction. Although various sparsifying transforms have been used in medical image reconstruction such as wavelet, contourlet, and total variation (TV) etc., the efficiency of these transforms typically rely on the special structure of the underlying image. A better way to address this issue is to develop an overcomplete dictionary from the input data in order to get a better sparsifying transform for the underlying image. However, the general overcomplete dictionaries do not satisfy the so-called perfect reconstruction property which ensures that the given signal can be perfectly represented by its canonical coefficients in a manner similar to orthonormal bases, resulting in time consuming in the iterative image reconstruction. This work is to develop an adaptive wavelet tight frame method for magnetic resonance image reconstruction. The proposed scheme incorporates the adaptive wavelet tight frame approach into the magnetic resonance image reconstruction by solving a l0-regularized minimization problem. Numerical results show that the proposed approach provides significant time savings as compared to the over-complete dictionary based methods with comparable performance in terms of both peak signal-to-noise ratio and subjective visual quality.
Highlights
Compressed sensing (CS)[1, 2] aims to reconstruct a signal, which is assumed to be sparse in a particular transform domain, from significantly fewer measurements than mandated by traditional Nyquist sampling
Various sparsifying transforms have been used in Magnetic resonance imaging (MRI) reconstruction such as wavelet[3], contourlet [4],and total variation (TV) [5] etc, the efficiency of these transforms typically rely on the special structure of the underlying image
We present a new way for MRI reconstruction by incorporating the two step with no reference images
Summary
Compressed sensing (CS)[1, 2] aims to reconstruct a signal, which is assumed to be sparse in a particular transform domain, from significantly fewer measurements than mandated by traditional Nyquist sampling. An alternating scheme introduced in [13] is implemented by imposing additional orthonormal constraint on the designed dictionary Owing to this constraint, the orthogonal dictionary learning-based algorithm for image processing [14] and MRI reconstruction [13] provides significant time saving and competitive result as compared K-SVD-based methods. Different from the patch-based transforms, a global basis, called adaptive tight wavelet frame, was proposed by Cai et al [15] for image denoising.
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