Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

By Ola Marius Lysaker, Arvid Lundervold, Xuecheng Tai. 2003

935 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

An overview of deep learning in medical imaging focusing on MRI (2018, methodology): “For example Bayesian Markov random field models [173], rough set theory [174], higherorder singular value decomposition [175], wavelets [176], independent component analysis [177], or higher order PDEs [178].”
A Combined First and Second Order Variational Approach for Image Reconstruction (2012, neutral): “[52,53], Chan et al.”
Fractional-Order Anisotropic Diffusion for Image Denoising (2007, background): “To reduce the blocky effect, while preserving sharp jump discontinuities (edges), many other non-linear ﬁlters have been suggested in the literature [10]–[18] and during the last few years, fourth-order PDEs have been of special interest [13]–[18].”
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional (2005, methodology): “However, both from a theoretical (Weickert, 1998; Ring, 2000) and experimental (Lysaker et al., 2003; Chambolle and Lions, 1997; Chan et al., 2000) point of view, it has been shown that the TV-norm transforms smooth signal into piecewise constants, the so-called staircase effect.”
An efficient algorithm for compressed MR imaging using total variation and wavelets (2008, methodology): “For example, introducing a fourth-order regularization term such as the one used in [ 19 ] to the objective function in (5) will certainly improve the quality of reconstructed images (enhancing the recovery of small-scale details); however, the resulting problem is too difficult to solve for real wo”
Implicit Neural Representations with Periodic Activation Functions (2020, methodology): “7, where we compare performance on texture images versus Deep Image Prior [41], Navier-Stokes, Fluid Dynamics Image Inpainting [7] (Diffusion), and SIRENs with no prior, total variation prior (TV), and Frobenius norm of Hessian [31, 30] priors (FH) respectively.”
Image Decomposition and Restoration Using Total Variation Minimization and the H1 (2003, background): “Related PDEs of fourth order, arising in image analysis, can be found, for instance, in [7], [12], and [11].”
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “Here we take the Lysaker-Lundervold-Tai (LLT) model [27] as an example.”
Denoising of Dynamic Contrast-Enhanced MR Images Using Dynamic Nonlocal Means (2010, background): “Denoising based on a higher order differential equation has also been proposed in the literature [ 26 ].”
Variable Exponent, Linear Growth Functionals in Image Restoration (2006, methodology): “We also refer the reader to the work in [15, 16, 26, 35] for an alternate variational approach for reducing staircasing by minimizing second order functionals.”
A survey on the magnetic resonance image denoising methods (2014, methodology): “The result of [21,22] shows that the fourth-order PDE and fourth-order adaptive PDE overcome this blocky effect by comparing with anisotropic diffusion filter in terms of SNR.”