ℓ2 − ℓ1 Fidelity based Elastic Net Regularisation for Magnetic Resonance Image Denoising

In this paper, we design an optimization problem for denoising 3 dimensional Magnetic Resonance Image (MRI) data. The problem is formulated as a variational technique considering the underlying distribution of noise to be Gaussian and Laplacian. We propose a mixed noise removal technique which simultaneously handles noise of two different nature rather than initially detecting impulse noise corrupted outlier pixels and then handling additive white Gaussian noise. This is made possible by the combination of ℓ
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data fidelity terms along with regularization penalty terms. We use elastic net regularization (combination of Total Variation (TV) and Tikhonov-Miller (TM) as two different regularization terms) to obtain better reconstruction quality. Experiments conducted on synthetically corrupted phantom brain MR data and real noisy knee MRI image obtained from patients show that our proposed technique outperforms comparing techniques even under higher intensity of noise levels.