Single Image Compressed Sensing MRI via a Self-Supervised Deep Denoising Approach

TL;DR

This work tackles the data-hungry nature and generalisability concerns of deep-learning–based CS-MRI by proposing a single-image, self-supervised framework that couples a CNN denoiser with a classical CS algorithm through a DeepRED-inspired ADMM objective. It defines a self-supervised loss based on $L_{kdc}$ and augments training with an ADMM split that incorporates a denoiser $g(\cdot)$, with options including BM3D or D-AMP to address nonlocal CS artefacts. Empirically, the approach—particularly the SS-D-AMP variant—achieves substantial PSNR gains (approximately $4.49$ dB on brains and $2.63$ dB on knees) over baselines and reduces per-epoch variability, while remaining compatible with existing CNN and CS methods. The method promises robust CS-MRI reconstructions without large training datasets and suggests future extensions to multi-coil data and GPU-accelerated denoisers for practical deployment.

Abstract

Popular methods in compressed sensing (CS) are dependent on deep learning (DL), where large amounts of data are used to train non-linear reconstruction models. However, ensuring generalisability over and access to multiple datasets is challenging to realise for real-world applications. To address these concerns, this paper proposes a single image, self-supervised (SS) CS-MRI framework that enables a joint deep and sparse regularisation of CS artefacts. The approach effectively dampens structured CS artefacts, which can be difficult to remove assuming sparse reconstruction, or relying solely on the inductive biases of CNN to produce noise-free images. Image quality is thereby improved compared to either approach alone. Metrics are evaluated using Cartesian 1D masks on a brain and knee dataset, with PSNR improving by 2-4dB on average.

Figures (5)

• Figure 1: Proposed single image, self-supervised training procedure. Each epoch, sampled $k$-space $\mathbf{y}_\Omega$ is divided into subsets $\mathbf{y}_\Lambda, \mathbf{y}_\Upsilon$. Image estimates $\hat{\mathbf{x}}_\Lambda = f(F_\Lambda^H\mathbf{y}_\Lambda | \Theta_k)$ and $\hat{\mathbf{x}}_\Omega = f(F_\Omega^H\mathbf{y}_\Omega|\Theta_k)$ are then generated. CNN and DC blocks are described in Eq. \ref{['eq:dccnn']}, where $\Theta_k = \{\theta_t\}_{t=1}^n$ at epoch $k$. The MSE between $\hat{\mathbf{x}}_\Lambda$ and the denoiser estimate $\mathbf{x}_k$ ($L_{CS} := \frac{\mu}{2} \|\mathbf{x}_k - \hat{\mathbf{x}}_\Lambda - \mathbf{q}_k \|_2^2$), as well as withheld $k$-space $\mathbf{y}_\Upsilon$ ($L_{kdc} := \| \mathbf{y}_\Upsilon - F_\Upsilon \mathbf{\hat{x}}_\Lambda \|_2^2$), are used to update $\mathrm{\Theta}$ (Eq. \ref{['eq:cnn']}). $\mathbf{q}_k$ is the Lagrange multipliers vector. Rather than relying on the inherent bias of CNN to produce noise-free images via $L_{kdc}$, inclusion of $L_{CS}$ ensures the solution is noise-free with respect to the chosen CS-MRI algorithm.
• Figure 1: Parameters used in experiments (found via grid-search). In SS-BM3D, denoiser standard deviation of noise is normalised between $\sigma \in [0, 1]$. We deploy $\sigma=0.012$. ConvDecoder parameters are as-per the original implementation darestani_accelerated_2021.
• Figure 2: Average performance achieved by each reconstruction method per dataset. PSNR (dB) SSIM (%).
• Figure 3: Representative reconstructions, comparing performance from our SS-based methods on the brain souza_open_2018 and knee knoll_fastmri_2020 datasets. SS alone is indicative of ZS-SSL yaman_zero-shot_2022.
• Figure 4: Representative test loss. Continuously randomizing $\Lambda, \Upsilon$ helps avoid overfitting. SS-D-AMP improves upon SS by stabilising epoch-to-epoch variations and incorporating the D-AMP reconstruction into the loss function (shown by red arrows).