access icon free Directional tensor product complex tight framelets for compressed sensing MRI reconstruction

Compressed sensing magnetic resonance imaging (CS-MRI) is an effective way of reducing the sampling data in the k-space and shortening the scanning time. Motivated by the high performance of directional tensor product complex tight framelets (TPCTFs) for the image denoising problem, the authors proposed a novel framework that integrated TPCTF for sparse representation and projected fast iterative soft-thresholding algorithm (pFISTA) for CS-MRI reconstruction. Furthermore, to take advantage of the cross-scale relations in the wavelet tree of frame coefficients, the bivariate shrinkage (BS) function with local variance estimation is proposed to shrink thresholding. Such TPCTFs can provide sparse directional representations very well for MR image. When compared with other the state-of-the-art CS-MRI algorithms in numerical experiments, the proposed TPCTF-BS method achieves a higher reconstruction quality with respect to image edge preservation and the artefact suppression.

Inspec keywords: image denoising; trees (mathematics); medical image processing; tensors; wavelet transforms; image reconstruction; compressed sensing; iterative methods; biomedical MRI; image representation

Other keywords: image edge preservation; soft-thresholding algorithm; projected fast iterative soft-thresholding algorithm; shrink thresholding; compressed sensing MRI reconstruction; bivariate shrinkage function; cross-scale relations; wavelet tree; image denoising problem; sparse directional representations; directional tensor product complex tight framelets; artefact suppression; compressed magnetic resonance imaging; CS-MRI reconstruction; local variance estimation

Subjects: Interpolation and function approximation (numerical analysis); Linear algebra (numerical analysis); Patient diagnostic methods and instrumentation; Algebra, set theory, and graph theory; Numerical approximation and analysis; Combinatorial mathematics; Optical, image and video signal processing; Combinatorial mathematics; Biomedical magnetic resonance imaging and spectroscopy; Integral transforms in numerical analysis; Medical magnetic resonance imaging and spectroscopy; Integral transforms in numerical analysis; Computer vision and image processing techniques; Biology and medical computing; Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis)

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