Phase retrieval based on shaped incoherent sources

By designing five different incoherent sources in ghost imaging(GI), we have proposed a kind of five-step phase-shifting method to reconstruct the phase distribution of the complicated object without the need of complicated GI system, iterative algorithm and Fourier transform step. The applicability of this theoretical proposal is demonstrated via numerical simulations with two kinds of complicated objects.

Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction

Recently, score-based diffusion models have shown satisfactory performance in MRI reconstruction. Most of these methods require a large amount of fully sampled MRI data as a training set, which, sometimes, is difficult to acquire in practice. This paper proposes a fully-sampled-data-free score-based diffusion model for MRI reconstruction, which learns the fully sampled MR image prior in a self-supervised manner on undersampled data. Specifically, we first infer the fully sampled MR image distribution from the undersampled data by Bayesian deep learning, then perturb the data distribution and approximate their probability density gradient by training a score function. Leveraging the learned score function as a prior, we can reconstruct the MR image by performing conditioned Langevin Markov chain Monte Carlo (MCMC) sampling. Experiments on the public dataset show that the proposed method outperforms existing self-supervised MRI reconstruction methods and achieves comparable performances with the conventional (fully sampled data trained) score-based diffusion methods.

One-shot Generative Prior Learned from Hankel-k-space for Parallel Imaging Reconstruction

Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space data. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the large Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from redundant and low-rank data space. At the iterative reconstruction stage, it is observed that the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency con-strain on the measurement data. Experimental results confirmed that the internal statistics of patches within a single k-space data carry enough information for learning a powerful generative model and provide state-of-the-art reconstruction.

K-UNN: k-Space Interpolation With Untrained Neural Network

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approach does not fully use the MR image physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier, regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can more accurately characterize the physical priors of MR images than existing traditional methods. Additionally, under a series of commonly used sampling trajectories, experiments also show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and even outperforms the state-of-the-art supervised-trained k-space deep learning methods in some cases.

Accelerating Magnetic Resonance Parametric Mapping Using Simultaneously Spatial Patch-based and Parametric Group-based Low-rank Tensors (SMART)

Quantitative magnetic resonance (MR) parametric mapping is a promising approach for characterizing intrinsic tissue-dependent information. However, long scan time significantly hinders its widespread applications. Recently, low-rank tensor has been employed and demonstrated good performance in accelerating MR parametricmapping. In this study, we propose a novel method that uses spatial patch-based and parametric group-based low rank tensors simultaneously (SMART) to reconstruct images from highly undersampled k-space data. The spatial patch-based low-rank tensor exploits the high local and nonlocal redundancies and similarities between the contrast images in parametric mapping. The parametric group based low-rank tensor, which integrates similar exponential behavior of the image signals, is jointly used to enforce the multidimensional low-rankness in the reconstruction process. In vivo brain datasets were used to demonstrate the validity of the proposed method. Experimental results have demonstrated that the proposed method achieves 11.7-fold and 13.21-fold accelerations in two-dimensional and three-dimensional acquisitions, respectively, with more accurate reconstructed images and maps than several state-of-the-art methods. Prospective reconstruction results further demonstrate the capability of the SMART method in accelerating MR quantitative imaging.

Robust Beamforming Design for IRS-Aided URLLC in D2D Networks

Intelligent reflecting surface (IRS) and device-to-device (D2D) communication are two promising technologies for improving transmission reliability between transceivers in communication systems. In this paper, we consider the design of reliable communication between the access point (AP) and actuators for a downlink multiuser multiple-input single-output (MISO) system in the industrial IoT (IIoT) scenario. We propose a two-stage protocol combining IRS with D2D communication so that all actuators can successfully receive the message from AP within a given delay. The superiority of the protocol is that the communication reliability between AP and actuators is doubly augmented by the IRS-aided first-stage transmission and the second-stage D2D transmission. A joint optimization problem of active and passive beamforming is formulated, which aims to maximize the number of actuators with successful decoding. We study the joint beamforming problem for cases where the channel state information (CSI) is perfect and imperfect. For each case, we develop efficient algorithms that include convergence and complexity analysis. Simulation results demonstrate the necessity and role of IRS with a well-optimized reflection matrix, and the D2D network in promoting reliable communication. Moreover, the proposed protocol can enable reliable communication even in the presence of stringent latency requirements and CSI estimation errors.

Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI

Recently, model-driven deep learning unrolls a certain iterative algorithm of a regularization model into a cascade network by replacing the first-order information (i.e., (sub)gradient or proximal operator) of the regularizer with a network module, which appears more explainable and predictable compared to common data-driven networks. Conversely, in theory, there is not necessarily such a functional regularizer whose first-order information matches the replaced network module, which means the network output may not be covered by the original regularization model. Moreover, up to now, there is also no theory to guarantee the global convergence and robustness (regularity) of unrolled networks under realistic assumptions. To bridge this gap, this paper propose to present a safeguarded methodology on network unrolling. Specifically, focusing on accelerated MRI, we unroll a zeroth-order algorithm, of which the network module represents the regularizer itself, so that the network output can be still covered by the regularization model. Furthermore, inspired by the ideal of deep equilibrium models, before backpropagating, we carry out the unrolled iterative network to converge to a fixed point to ensure the convergence. In case the measurement data contains noise, we prove that the proposed network is robust against noisy interference. Finally, numerical experiments show that the proposed network consistently outperforms the state-of-the-art MRI reconstruction methods including traditional regularization methods and other deep learning methods.

RIS-aided D2D Communication Design for URLLC Packet Delivery

In this paper, we consider a smart factory scenario where a set of actuators receive critical control signals from an access point (AP) with reliability and low latency requirements. We investigate jointly active beamforming at the AP and passive phase shifting at the reconfigurable intelligent surface (RIS) for successfully delivering the control signals from the AP to the actuators within a required time duration. The transmission follows a two-stage design. In the first stage, each actuator can both receive the direct signal from AP and the reflected signal from the RIS. In the second stage, the actuators with successful reception in the first stage, relay the message through the D2D network to the actuators with failed receptions. We formulate a non-convex optimization problem where we first obtain an equivalent but more tractable form by addressing the problem with discrete indicator functions. Then, Frobenius inner product based equality is applied for decoupling the optimization variables. Further, we adopt a penalty-based approach to resolve the rank-one constraints. Finally, we deal with the $\ell_0$-norm by $\ell_1$-norm approximation and add an extra term $\ell_1-\ell_2$ for sparsity. Numerical results reveal that the proposed two-stage RIS-aided D2D communication protocol is effective for enabling reliable communication with latency requirements.