MRI denoising with a non‐blind deep complex‐valued convolutional neural network

MR images with high signal-to-noise ratio (SNR) provide more diagnostic information. Various methods for MRI denoising have been developed, but the majority of them operate on the magnitude image and neglect the phase information. Therefore, the goal of this work is to design and implement a complex-valued convolutional neural network (CNN) for MRI denoising. A complex-valued CNN incorporating the noise level map (non-blind <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ℂ</mml:mi></mml:mrow> <mml:annotation>$$ \mathbb{C} $$</mml:annotation></mml:semantics> </mml:math> DnCNN) was trained with ground truth and simulated noise-corrupted image pairs. The proposed method was validated using both simulated and in vivo data collected from low-field scanners. Its denoising performance was quantitively and qualitatively evaluated, and it was compared with the real-valued CNN and several other algorithms. For the simulated noise-corrupted testing dataset, the complex-valued models had superior normalized root-mean-square error, peak SNR, structural similarity index, and phase ABSD. By incorporating the noise level map, the non-blind <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ℂ</mml:mi></mml:mrow> <mml:annotation>$$ \mathbb{C} $$</mml:annotation></mml:semantics> </mml:math> DnCNN showed better performance in dealing with spatially varying parallel imaging noise. For in vivo low-field data, the non-blind <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ℂ</mml:mi></mml:mrow> <mml:annotation>$$ \mathbb{C} $$</mml:annotation></mml:semantics> </mml:math> DnCNN significantly improved the SNR and visual quality of the image. The proposed non-blind <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ℂ</mml:mi></mml:mrow> <mml:annotation>$$ \mathbb{C} $$</mml:annotation></mml:semantics> </mml:math> DnCNN provides an efficient and effective approach for MRI denoising. This is the first application of non-blind <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ℂ</mml:mi></mml:mrow> <mml:annotation>$$ \mathbb{C} $$</mml:annotation></mml:semantics> </mml:math> DnCNN to medical imaging. The method holds the potential to enable improved low-field MRI, facilitating enhanced diagnostic imaging in under-resourced areas.