Although MRI reconstruction requires a dealiasing transformation from undersampled to fully-sampled data, task-agnostic diffusion priors sample images via a denoising-based generative trajectory from an asymptotic start-point of Gaussian noise onto fully-sampled data. Since aliasing artifacts in MR images carry spatial structure deviating from Gaussian noise, this noise-governed trajectory can cause suboptimal artifact suppression. To address this limitation, we introduce the first Fourier-constrained diffusion bridge (FDB) for MRI reconstruction in the literature. Unlike task-agnostic diffusion priors, FDB does not rely on noise in its forward process and instead learns a dealiasing transformation between a start-point of undersampled data and the end-point of fully-sampled data. The start-point is derived via a stochastic Fourier-constrained degradation operator that removes a progressively growing set of spatial frequencies. Unlike cold/soft diffusion priors that use an asymptotic start-point of severely degraded measurements, FDB uses a realistically undersampled start-point to ensure closer alignment of model input between training and test distributions. Unlike existing diffusion bridges that use degradations based on weighted linear averages and noise addition, FDB implements degradations based on binary removal of compact k-space sets to conform to the physics of accelerated MRI. To further improve image quality, FDB leverages a novel sampling algorithm based on progressive dealiasing by continually correcting recovered k-space data across reverse diffusion steps. Demonstrations on brain MRI show that FDB outperforms competing methods by 4.5dB PSNR and 8.3% SSIM in within-domain and by 4.7dB PSNR and 16.4% SSIM in cross-domain reconstructions.

Magnetic particle imaging (MPI) offers unparalleled contrast and resolution for tracing magnetic nanoparticles. A common imaging procedure calibrates a system matrix (SM) that is used to reconstruct data from subsequent scans. The ill-posed reconstruction problem can be solved by simultaneously enforcing data consistency based on the SM and regularizing the solution based on an image prior. Traditional hand-crafted priors cannot capture the complex attributes of MPI images, whereas recent MPI methods based on learned priors can suffer from extensive inference times or limited generalization performance. Here, we introduce a novel physics-driven method for MPI reconstruction based on a deep equilibrium model with learned data consistency (DEQ-MPI). DEQ-MPI reconstructs images by augmenting neural networks into an iterative optimization, as inspired by unrolling methods in deep learning. Yet, conventional unrolling methods are computationally restricted to few iterations resulting in non-convergent solutions, and they use hand-crafted consistency measures that can yield suboptimal capture of the data distribution. DEQ-MPI instead trains an implicit mapping to maximize the quality of a convergent solution, and it incorporates a learned consistency measure to better account for the data distribution. Demonstrations on simulated and experimental data indicate that DEQ-MPI achieves superior image quality and competitive inference time to state-of-the-art MPI reconstruction methods.

Single pixel imaging (SPI) enables high-resolution imaging through multiple coded measurements based on low-resolution snapshots. An inverse problem can then be solved to reconstruct a high-resolution image given the coded measurements. There has been recent interest in adoption of deep neural networks in SPI reconstruction. However, existing methods are commonly trained with pixel-wise loss terms such as the ℓ1-norm loss, which can result in spatial blurring and poor sensitivity to structural details. In this study, we propose a novel approach for deep SPI reconstruction based on an unrolled conditional generative adversarial network (cGAN) model. The generator estimates the high-resolution image using coded low-resolution measurements by iterating across a cascade of denoising and data-consistency modules. Meanwhile, the discriminator distinguishes real versus synthesized high-resolution images. The architecture is trained end-to-end via a combined pixel-wise and adversarial loss to enhance sensitivity to structural details. The proposed method is demonstrated against existing SPI reconstruction methods, and ablation studies are performed to demonstrate the individual model components. The proposed method outperforms competing methods in terms of both quantitative metrics and visual quality.

Imputation of missing images via source-to-target modality translation can improve diversity in medical imaging protocols. A pervasive approach for synthesizing target images involves one-shot mapping through generative adversarial networks (GAN). Yet, GAN models that implicitly characterize the image distribution can suffer from limited sample fidelity. Here, we propose a novel method based on adversarial diffusion modeling, SynDiff, for improved performance in medical image translation. To capture a direct correlate of the image distribution, SynDiff leverages a conditional diffusion process that progressively maps noise and source images onto the target image. For fast and accurate image sampling during inference, large diffusion steps are taken with adversarial projections in the reverse diffusion direction. To enable training on unpaired datasets, a cycle-consistent architecture is devised with coupled diffusive and non-diffusive modules that bilaterally translate between two modalities. Extensive assessments are reported on the utility of SynDiff against competing GAN and diffusion models in multi-contrast MRI and MRI-CT translation. Our demonstrations indicate that SynDiff offers quantitatively and qualitatively superior performance against competing baselines.

Summary In the direction of arrival (DoA) estimation, typically sensor arrays are used where the number of required sensors can be large depending on the application. With the help of compressed sensing (CS), hardware complexity of the sensor array system can be reduced since reliable estimations are possible by using the compressed measurements where the compression is done by measurement matrices. After the compression, DoAs are reconstructed by using sparsity promoting algorithms such as alternating direction method of multipliers (ADMM). For the given procedure, both the measurement matrix design and the reconstruction algorithm may include computationally intensive operations, which are addressed in this study. The presented simulation results imply the feasibility of the system in real‐time processing with energy efficient implementations. We propose employing parallel programming to satisfy the real‐time processing requirements. While the measurement matrix design has been accelerated 16 with CPU based parallel version with respect to the fastest serial implementation, ADMM based DoA estimation has been improved 1.1 with GPU based parallel version compared to the fastest CPU parallel implementation. In addition, we achieved, to the best of our knowledge, the first energy‐efficient real‐time DoA estimation on embedded Jetson GPGPUs in 15 W power consumption without affecting the DoA accuracy performance.

Magnetic particle imaging (MPI) offers exceptional contrast for magnetic nanoparticles (MNP) at high spatio-temporal resolution. A common procedure in MPI starts with a calibration scan to measure the system matrix (SM), which is then used to set up an inverse problem to reconstruct images of the MNP distribution during subsequent scans. This calibration enables the reconstruction to sensitively account for various system imperfections. Yet time-consuming SM measurements have to be repeated under notable changes in system properties. Here, we introduce a novel deep learning approach for accelerated MPI calibration based on Transformers for SM super-resolution (TranSMS). Low-resolution SM measurements are performed using large MNP samples for improved signal-to-noise ratio efficiency, and the high-resolution SM is super-resolved via model-based deep learning. TranSMS leverages a vision transformer module to capture contextual relationships in low-resolution input images, a dense convolutional module for localizing high-resolution image features, and a data-consistency module to ensure measurement fidelity. Demonstrations on simulated and experimental data indicate that TranSMS significantly improves SM recovery and MPI reconstruction for up to 64-fold acceleration in two-dimensional imaging.

Superparamagnetic iron oxide nanoparticles (SPIONs) have a high potential for use in clinical diagnostic and therapeutic applications. In vivo distribution of SPIONs can be imaged with the Magnetic Particle Imaging (MPI) method, which uses an inhomogeneous magnetic field with a field free region (FFR). The spatial distribution of the SPIONs are obtained by scanning the FFR inside the field of view (FOV) and sensing SPION related magnetic field disturbance. MPI magnets can be configured to generate a field free point (FFP), or a field free line (FFL) to scan the FOV. FFL scanners provide more sensitivity, and are also more suitable for scanning large regions compared to FFP scanners. Interventional procedures will benefit greatlyfrom FFL based open magnet configurations. Here, we present the first open-sided MPI system that can electronically scan the FOV with an FFL to generate tomographic MPI images. Magnetic field measurements show that FFL can be rotated electronically in the horizontal plane and translated in three dimensions to generate 3D MPI images. Using the developed scanner, we obtained 2D images of dot and cylinder phantoms with varying iron concentrations between 11 μg/ml and 770 μg/ml. We used a measurement based system matrix image reconstruction method that minimizes 11-norm and total variation in the images. Furthermore, we present 2D imaging results of two 4 mm-diameter vessel phantoms with 0% and 75% stenosis. The experiments show high quality imaging results with a resolution down to 2.5 mm for a relatively low gradient field of 0.6 T/m.

We deal with reconstruction of convolved images with known point spread functions. We adopt a feature enhanced deconvolution method. Instead of using a pre-designed sparsifying transform, we use an online transform learning based method, and reconstruct images along with a sparsifying transform. To avoid circular effects, we implement non-circular convolution operator using FFT based convolution and dead pixels. We use a coordinate descent type algorithm and derive the associated update steps for both circular and non-circular deconvolution. Moreover, we show single image super-resolution extension for non-circular deconvolution. We compare the proposed method to other feature enhanced deconvolution alternatives, as well as conventional methods such as Lucy-Richardson method. Finally, we demonstrate the effectiveness of the algorithm for circular deconvolution, non-circular deconvolution, and single-image super-resolution applications.

Magnetic particle imaging (MPI) is a relatively new medical imaging modality, which detects the nonlinear response of magnetic nanoparticles (MNPs) that are exposed to external magnetic fields. The system matrix (SM) method for MPI image reconstruction requires a time consuming system calibration scan prior to image acquisition, where a single MNP sample is measured at each voxel position in the field-of-view (FOV). The scanned sample has the maximum size of a voxel so that the calibration measurements have relatively poor signal-to-noise ratio (SNR). In this paper, we present the coded calibration scene (CCS) framework, where we place multiple MNP samples inside the FOV in a random or pseudo-random fashion. Taking advantage of the sparsity of the SM, we reconstruct the SM by solving a convex optimization problem with alternating direction method of multipliers using CCS measurements. We analyze the effects of filling rate, number of measurements, and SNR on the SM reconstruction using simulations and demonstrate different implementations of CCS for practical realization. We also compare the imaging performance of the proposed framework with that of a standard compressed sensing SM reconstruction that utilizes a subset of calibration measurements from a single MNP sample. The results show that CCS significantly reduces calibration time while increasing both the SM reconstruction and image reconstruction performances.

A central limitation of multiple-acquisition magnetic resonance imaging (MRI) is the degradation in scan efficiency as the number of distinct datasets grows. Sparse recovery techniques can alleviate this limitation via randomly undersampled acquisitions. A frequent sampling strategy is to prescribe for each acquisition a different random pattern drawn from a common sampling density. However, naive random patterns often contain gaps or clusters across the acquisition dimension that, in turn, can degrade reconstruction quality or reduce scan efficiency. To address this problem, a statistically segregated sampling method is proposed for multiple-acquisition MRI. This method generates multiple patterns sequentially while adaptively modifying the sampling density to minimize k-space overlap across patterns. As a result, it improves incoherence across acquisitions while still maintaining similar sampling density across the radial dimension of k-space. Comprehensive simulations and in vivo results are presented for phase-cycled balanced steady-state free precession and multi-echo [Formula: see text]-weighted imaging. Segregated sampling achieves significantly improved quality in both Fourier and compressed-sensing reconstructions of multiple-acquisition datasets.

In this study, we propose a novel algorithm for compressive imaging using digital micromirror device (DMD) modulated focal plane array (FPA) data. In this setting, DMD modulates the scene in the image domain by blocking some of the pixels at a higher resolution level. For reconstruction, a regularized optimization problem is solved, whereas reconstruction time is crucial for a practical compressive sensing application. Here, we propose an augmented Lagrangian based method that employs sparsity in both Fourier and gradient spaces, where we apply a separate proximal mapping for each snapshot. We demonstrate the performance of the algorithm via comparison to the state-of-the-art. The proposed method yields higher pSNR at shorter convergence times, especially at higher compression ratios.

We present an Augmented Lagrangian Method (ALM) for solving image reconstruction problems with a cost function consisting of multiple regularization functions with a data fidelity constraint. The presented technique is used to solve inverse problems related to image reconstruction, including compressed sensing formulations. Our contributions include an improvement for reducing the number of computations required by an existing ALM method, an approach for obtaining the proximal mapping associated with p-norm based regularizers, and lastly a particular ALM for the constrained image reconstruction problem with a hybrid cost function including a weighted sum of the p-norm and the total variation of the image. We present examples from Synthetic Aperture Radar imaging and Computed Tomography.