Deep unfolding as iterative regularization for imaging inverse problems

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have better interpretability and performance. However, to our knowledge, their accuracy and stability in solving inverse problems cannot be fully guaranteed. To bridge this gap, we modified the training procedure and proved that the unfolding method is an iterative regularization method. More precisely, we jointly learn a convex penalty function adversarially by an input-convex neural network (ICNN) to characterize the distance to a real data manifold and train a DNN unfolded from the proximal gradient descent algorithm with this learned penalty. Suppose the real data manifold intersects the inverse problem solutions with only the unique real solution. We prove that the unfolded DNN will converge to it stably. Furthermore, we demonstrate with an example of MRI reconstruction that the proposed method outperforms conventional unfolding methods and traditional regularization methods in terms of reconstruction quality, stability and convergence speed

Enhancing the number of modes in metasurfaced reverberation chambers for field uniformity improvement

The use of metasurfaces to increase the number of modes, lower the operating frequency, and improve the field uniformity in reverberation chambers (RCs) is investigated in this paper. The method used to improve the field uniformity and decrease the resonance frequencies is based on increasing the number of modes by using the concept of subwavelength cavities. The resonance frequencies of a RC with metasurface wall are derived and expressed analytically in terms of macroscopic characteristics. Simulation of the reflection phase of the unit cell is then given as a guideline to choose the required microscopic parameters of the designed metasurface. The mode density in such subwavelength RCs is then obtained using a numerical eigenmode solver. Compared to traditional RCs, a much higher modal density is obtained at low frequencies. The standard deviation of the field uniformity in the test volume of the RC corresponding to different types of metasurface walls is finally compared. It is shown that by increasing the number of modes in the RC at the lower band, the operating frequency decreases and the field uniformity of the RC is improved

SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI

Diffusion models are a leading method for image generation and have been successfully applied in magnetic resonance imaging (MRI) reconstruction. Current diffusion-based reconstruction methods rely on coil sensitivity maps (CSM) to reconstruct multi-coil data. However, it is difficult to accurately estimate CSMs in practice use, resulting in degradation of the reconstruction quality. To address this issue, we propose a self-consistency-driven diffusion model inspired by the iterative self-consistent parallel imaging (SPIRiT), namely SPIRiT-Diffusion. Specifically, the iterative solver of the self-consistent term in SPIRiT is utilized to design a novel stochastic differential equation (SDE) for diffusion process. Then $\textit{k}$-space data can be interpolated directly during the reverse diffusion process, instead of using CSM to separate and combine individual coil images. This method indicates that the optimization model can be used to design SDE in diffusion models, driving the diffusion process strongly conforming with the physics involved in the optimization model, dubbed model-driven diffusion. The proposed SPIRiT-Diffusion method was evaluated on a 3D joint Intracranial and Carotid Vessel Wall imaging dataset. The results demonstrate that it outperforms the CSM-based reconstruction methods, and achieves high reconstruction quality at a high acceleration rate of 10

Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and robustness. In response, we introduce Convex Latent-Optimized Adversarial Regularizers (CLEAR), a novel and interpretable data-driven paradigm. CLEAR represents a fusion of deep learning (DL) and variational regularization. Specifically, we employ a latent optimization technique to adversarially train an input convex neural network, and its set of minima can fully represent the real data manifold. We utilize it as a convex regularizer to formulate a CLEAR-informed variational regularization model that guides the solution of the imaging inverse problem on the real data manifold. Leveraging its inherent convexity, we have established the convergence of the projected subgradient descent algorithm for the CLEAR-informed regularization model. This convergence guarantees the attainment of a unique solution to the imaging inverse problem, subject to certain assumptions. Furthermore, we have demonstrated the robustness of our CLEAR-informed model, explicitly showcasing its capacity to achieve stable reconstruction even in the presence of measurement interference. Finally, we illustrate the superiority of our approach using MRI reconstruction as an example. Our method consistently outperforms conventional data-driven techniques and traditional regularization approaches, excelling in both reconstruction quality and robustness

Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI

Recently, regularization model-driven deep learning (DL) has gained significant attention due to its ability to leverage the potent representational capabilities of DL while retaining the theoretical guarantees of regularization models. However, most of these methods are tailored for supervised learning scenarios that necessitate fully sampled labels, which can pose challenges in practical MRI applications. To tackle this challenge, we propose a self-supervised DL approach for accelerated MRI that is theoretically guaranteed and does not rely on fully sampled labels. Specifically, we achieve neural network structure regularization by exploiting the inherent structural low-rankness of the $k$-space data. Simultaneously, we constrain the network structure to resemble a nonexpansive mapping, ensuring the network's convergence to a fixed point. Thanks to this well-defined network structure, this fixed point can completely reconstruct the missing $k$-space data based on matrix completion theory, even in situations where full-sampled labels are unavailable. Experiments validate the effectiveness of our proposed method and demonstrate its superiority over existing self-supervised approaches and traditional regularization methods, achieving performance comparable to that of supervised learning methods in certain scenarios

Sex‐specific activation of SK current by isoproterenol facilitates action potential triangulation and arrhythmogenesis in rabbit ventricles

Sex has a large influence on cardiac electrophysiological properties. Whether sex differences exist in apamin‐sensitive small conductance Ca2+‐activated K+ (SK) current (IKAS) remains unknown. We performed optical mapping, transmembrane potential, patch clamp, western blot and immunostaining in 62 normal rabbit ventricles, including 32 females and 30 males. IKAS blockade by apamin only minimally prolonged action potential (AP) duration (APD) in the basal condition for both sexes, but significantly prolonged APD in the presence of isoproterenol in females. Apamin prolonged APD at the level of 25% repolarization (APD25) more prominently than APD at the level of 80% repolarization (APD80), consequently reversing isoproterenol‐induced AP triangulation in females. In comparison, apamin prolonged APD to a significantly lesser extent in males and failed to restore the AP plateau during isoproterenol infusion. IKAS in males did not respond to the L‐type calcium current agonist BayK8644, but was amplified by the casein kinase 2 (CK2) inhibitor 4,5,6,7‐tetrabromobenzotriazole. In addition, whole‐cell outward IKAS densities in ventricular cardiomyocytes were significantly larger in females than in males. SK channel subtype 2 (SK2) protein expression was higher and the CK2/SK2 ratio was lower in females than in males. IKAS activation in females induced negative intracellular Ca2+–voltage coupling, promoted electromechanically discordant phase 2 repolarization alternans and facilitated ventricular fibrillation (VF). Apamin eliminated the negative Ca2+–voltage coupling, attenuated alternans and reduced VF inducibility, phase singularities and dominant frequencies in females, but not in males. We conclude that β‐adrenergic stimulation activates ventricular IKAS in females to a much greater extent than in males. IKAS activation plays an important role in ventricular arrhythmogenesis in females during sympathetic stimulation