K-space Measurements Research Articles

SPICER: Self-supervised learning for MRI with automatic coil sensitivity estimation and reconstruction.

To introduce a novel deep model-based architecture (DMBA), SPICER, that uses pairs of noisy and undersampled k-space measurements of the same object to jointly train a model for MRI reconstruction and automatic coil sensitivity estimation. SPICER consists of two modules to simultaneously reconstructs accurate MR images and estimates high-quality coil sensitivity maps (CSMs). The first module, CSM estimation module, uses a convolutional neural network (CNN) to estimate CSMs from the raw measurements. The second module, DMBA-based MRI reconstruction module, forms reconstructed images from the input measurements and the estimated CSMs using both the physical measurement model and learned CNN prior. With the benefit of our self-supervised learning strategy, SPICER can be efficiently trained without any fully sampled reference data. We validate SPICER on both open-access datasets and experimentally collected data, showing that it can achieve state-of-the-art performance in highly accelerated data acquisition settings (up to ). Our results also highlight the importance of different modules of SPICER-including the DMBA, the CSM estimation, and the SPICER training loss-on the final performance of the method. Moreover, SPICER can estimate better CSMs than pre-estimation methods especially when the ACS data is limited. Despite being trained on noisy undersampled data, SPICER can reconstruct high-quality images and CSMs in highly undersampled settings, which outperforms other self-supervised learning methods and matches the performance of the well-known E2E-VarNet trained on fully sampled ground-truth data.

IMJENSE: Scan-Specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI.

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

On retrospective k-space subsampling schemes for deep MRI reconstruction

Acquiring fully-sampled MRI k-space data is time-consuming, and collecting accelerated data can reduce the acquisition time. Employing 2D Cartesian-rectilinear subsampling schemes is a conventional approach for accelerated acquisitions; however, this often results in imprecise reconstructions, even with the use of Deep Learning (DL), especially at high acceleration factors. Non-rectilinear or non-Cartesian trajectories can be implemented in MRI scanners as alternative subsampling options. This work investigates the impact of the k-space subsampling scheme on the quality of reconstructed accelerated MRI measurements produced by trained DL models. The Recurrent Variational Network (RecurrentVarNet) was used as the DL-based MRI-reconstruction architecture. Cartesian, fully-sampled multi-coil k-space measurements from three datasets were retrospectively subsampled with different accelerations using eight distinct subsampling schemes: four Cartesian-rectilinear, two Cartesian non-rectilinear, and two non-Cartesian. Experiments were conducted in two frameworks: scheme-specific, where a distinct model was trained and evaluated for each dataset-subsampling scheme pair, and multi-scheme, where for each dataset a single model was trained on data randomly subsampled by any of the eight schemes and evaluated on data subsampled by all schemes. In both frameworks, RecurrentVarNets trained and evaluated on non-rectilinearly subsampled data demonstrated superior performance, particularly for high accelerations. In the multi-scheme setting, reconstruction performance on rectilinearly subsampled data improved when compared to the scheme-specific experiments. Our findings demonstrate the potential for using DL-based methods, trained on non-rectilinearly subsampled measurements, to optimize scan time and image quality.

Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models.

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method, different from conventional deep learning-based MRI reconstruction techniques. In addition to the maximum a posteriori estimate for the image, which can be obtained by maximizing the log-likelihood indirectly or directly, the minimum mean square error estimate and uncertainty maps can also be computed from those drawn samples. The data-driven Markov chains are constructed with the score-based generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. We numerically investigate the framework from these perspectives: (1)the interpretation of the uncertainty of the image reconstructed from undersampled k-space; (2) the effect of the number of noise scales used to train the generative models; (3) using a burn-in phase in MCMC sampling to reduce computation; (4) the comparison to conventional -wavelet regularized reconstruction; (5) the transferability of learned information; and (6) the comparison to fastMRI challenge. A framework is described that connects the diffusion process and advanced generative models with Markov chains. We demonstrate its flexibility in terms of contrasts and sampling patterns using advanced generative priors and the benefits of also quantifying the uncertainty for every pixel.

K-space and image domain collaborative energy-based model for parallel MRI reconstruction

Decreasing magnetic resonance (MR) image acquisition times can potentially make MR examinations more accessible. Prior arts including the deep learning models have been devoted to solving the problem of long MRI imaging time. Recently, deep generative models have exhibited great potentials in algorithm robustness and usage flexibility. Nevertheless, none of existing schemes can be learned from or employed to the k-space measurement directly. Furthermore, how do the deep generative models work well in hybrid domain is also worth being investigated. In this work, by taking advantage of the deep energy-based models, we propose a k-space and image domain collaborative generative model to comprehensively estimate the MR data from under-sampled measurement. Equipped with parallel and sequential orders, experimental comparisons with the state-of-the-arts demonstrated that they involve less error in reconstruction accuracy and are more stable under different acceleration factors.

A Self-Supervised Deep Learning Reconstruction for Shortening the Breathhold and Acquisition Window in Cardiac Magnetic Resonance Fingerprinting.

The aim of this study is to shorten the breathhold and diastolic acquisition window in cardiac magnetic resonance fingerprinting (MRF) for simultaneous T1, T2, and proton spin density (M0) mapping to improve scan efficiency and reduce motion artifacts. To this end, a novel reconstruction was developed that combines low-rank subspace modeling with a deep image prior, termed DIP-MRF. A system of neural networks is used to generate spatial basis images and quantitative tissue property maps, with training performed using only the undersampled k-space measurements from the current scan. This approach avoids difficulties with obtaining in vivo MRF training data, as training is performed de novo for each acquisition. Calculation of the forward model during training is accelerated by using GRAPPA operator gridding to shift spiral k-space data to Cartesian grid points, and by using a neural network to rapidly generate fingerprints in place of a Bloch equation simulation. DIP-MRF was evaluated in simulations and at 1.5 T in a standardized phantom, 18 healthy subjects, and 10 patients with suspected cardiomyopathy. In addition to conventional mapping, two cardiac MRF sequences were acquired, one with a 15-heartbeat(HB) breathhold and 254 ms acquisition window, and one with a 5HB breathhold and 150 ms acquisition window. In simulations, DIP-MRF yielded decreased nRMSE compared to dictionary matching and a sparse and locally low rank (SLLR-MRF) reconstruction. Strong correlation (R2 > 0.999) with T1 and T2 reference values was observed in the phantom using the 5HB/150 ms scan with DIP-MRF. DIP-MRF provided better suppression of noise and aliasing artifacts in vivo, especially for the 5HB/150 ms scan, and lower intersubject and intrasubject variability compared to dictionary matching and SLLR-MRF. Furthermore, it yielded a better agreement between myocardial T1 and T2 from 15HB/254 ms and 5HB/150 ms MRF scans, with a bias of −9 ms for T1 and 2 ms for T2. In summary, this study introduces an extension of the deep image prior framework for cardiac MRF tissue property mapping, which does not require pre-training with in vivo scans, and has the potential to reduce motion artifacts by enabling a shortened breathhold and acquisition window.

Accelerating multi-echo chemical shift encoded water-fat MRI using model-guided deep learning.

To accelerate chemical shift encoded (CSE) water-fat imaging by applying a model-guided deep learning water-fat separation (MGDL-WF) framework to the undersampled k-space data. A model-guided deep learning water-fat separation framework is proposed for the acceleration using Cartesian/radial undersampling data. The proposed MGDL-WF combines the power of CSE water-fat imaging model and data-driven deep learning by jointly using a multi-peak fat model and a modified residual U-net network. The model is used to guide the image reconstruction, and the network is used to capture the artifacts induced by the undersampling. A data consistency layer is used in MGDL-WF to ensure the output images to be consistent with the k-space measurements. A Gauss-Newton iteration algorithm is adapted for the gradient updating of the networks. Compared with the compressed sensing water-fat separation (CS-WF) algorithm/2-step procedure algorithm, the MGDL-WF increased peak signal-to-noise ratio (PSNR) by 5.31/5.23, 6.11/4.54, and 4.75dB/1.88dB with Cartesian sampling, and by 4.13/6.53, 2.90/4.68, and 1.68dB/3.48dB with radial sampling, at acceleration rates (R) of 4, 6, and 8, respectively. By using MGDL-WF, radial sampling increased the PSNR by 2.07dB at R=8, compared with Cartesian sampling. The proposed MGDL-WF enables exploiting features of the water images and fat images from the undersampled multi-echo data, leading to improved performance in the accelerated CSE water-fat imaging. By using MGDL-WF, radial sampling can further improve the image quality with comparable scan time in comparison with Cartesian sampling.

A k-space-based method to measure and correct for temporal B0 field variations in MR temperature imaging.

Present a method to use change in phase in repeated Cartesian k-space measurements to monitor the change in magnetic field for dynamic MR temperature imaging. The method is applied to focused ultrasound heating experiments in a gelatin phantom and an ex vivo salt pork sample, without and with simulated respiratory motion. In each experiment, phase variations due to B0 field drift and respiration were readily apparent in the measured phase difference. With correction, the SD of the temperature over time was reduced from 0.18°C to 0.14°C (no breathing) and from 0.81°C to 0.22°C (with breathing) for the gelatin phantom, and from 0.68°C to 0.13°C (no breathing) and from 1.06°C to 0.17°C (with breathing) for the pork sample. The accuracy in nonheated regions, assessed as the RMS error deviation from 0°C, improved from 1.70°C to 1.11°C (no breathing) and from 4.73°C to 1.47°C (with breathing) for the gelatin phantom, and from 5.95°C to 0.88°C (no breathing) and from 13.40°C to 1.73°C (with breathing) for the pork sample. The correction did not affect the temperature measurement accuracy in the heated regions. This work demonstrates that phase changes resulting from variations in B0 due to drift and respiration, commonly seen in MR thermometry applications, can be measured directly from 3D Cartesian acquisition methods. The correction of temporal field variations using the presented technique improved temperature accuracy, reduced variability in nonheated regions, and did not reduce accuracy in heated regions.

Non-Hermitian metasurface with non-trivial topology

Abstract The synergy between topology and non-Hermiticity in photonics holds immense potential for next-generation optical devices that are robust against defects. However, most demonstrations of non-Hermitian and topological photonics have been limited to super-wavelength scales due to increased radiative losses at the deep-subwavelength scale. By carefully designing radiative losses at the nanoscale, we demonstrate a non-Hermitian plasmonic–dielectric metasurface in the visible with non-trivial topology. The metasurface is based on a fourth order passive parity-time symmetric system. The designed device exhibits an exceptional concentric ring in its momentum space and is described by a Hamiltonian with a non-Hermitian Z 3 ${\mathbb{Z}}_{3}$ topological invariant of V = −1. Fabricated devices are characterized using Fourier-space imaging for single-shot k-space measurements. Our results demonstrate a way to combine topology and non-Hermitian nanophotonics for designing robust devices with novel functionalities.

Fast data-driven learning of parallel MRI sampling patterns for large scale problems

In this study, a fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. BASS is applicable when Cartesian fully-sampled k-space measurements of specific anatomy are available for training and the reconstruction method for undersampled measurements is specified; such information is used to define the efficacy of any SP for recovering the values at the non-sampled k-space points. BASS produces a sequence of SPs with the aim of finding one of a specified size with (near) optimal efficacy. BASS was tested with five reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Three datasets were used for testing, two of high-resolution brain images (text {T}_{2}-weighted images and, respectively, text {T}_{1rho }-weighted images) and another of knee images for quantitative mapping of the cartilage. The proposed approach has low computational cost and fast convergence; in the tested cases it obtained SPs up to 50 times faster than the currently best greedy approach. Reconstruction quality increased by up to 45% over that provided by variable density and Poisson disk SPs, for the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Quantitative MRI and prospective accelerated MRI results show improvements. Compared with greedy approaches, BASS rapidly learns effective SPs for various reconstruction methods, using larger SPs and larger datasets; enabling better selection of sampling-reconstruction pairs for specific MRI problems.

Multiscale wavelet-based regularized reconstruction algorithm for three-dimensional compressed sensing magnetic resonance imaging

Nowadays, the most dynamic and safe imaging technique used in hospitals to diagnose is magnetic resonance imaging (MRI). In clinical applications, such as follow-up of patients with planning surgery, radiation therapy, therapy response in bone metastases assessment and treatment for brain disorders, repeated MRI scans are performed. Unfortunately, the slow acquisitions of MRI drive cost high by limiting patient throughput as well as limiting the potential indications for use. A mathematical framework called compressed sensing (CS) to accelerate MRI acquisition is used for generating undersampled measurements. Then, the iterative nonlinear numerical method is required for perfect reconstruction from highly undersampled measurements. In this work, the multiscale wavelet domain regularization prior-based iterative reconstruction algorithm is developed to address the above-mentioned reconstruction problem, in which multiscale wavelet domain generalized Gaussian mixture model is utilized for the regularization prior. The regularization-based algorithm is applied to generate three-dimensional (3D) high-quality MRI volume from multichannel k-space measurements in a compressed sensing framework. Several experiments using one synthetic and one real 3D CS multichannel k-space data were used to evaluate and validate the performance of the proposed algorithm. The total variation (TV)-based and soft-thresholding (ST) based-reconstruction methods were implemented to compare with the proposed algorithm. Extensive experimental results demonstrated that the proposed method has improved results in terms of visual quality and quantitative measurements compared to the existing methods.

Compressed sensing regularized calibrationless parallel magnetic resonance imaging via deep learning

The longer scanning time requirement in Magnetic Resonance Imaging (MRI) can one way be overcome through parallel data acquisition technique. The scanning time in pMRI systems can further be reduced through calibrationless data acquisition process that eliminates the need of extra k-space data. Compressed Sensing (CS) or Compressive Sampling in data acquisition again reduces this scanning time as image reconstruction is done from the undersampled k-space measurements. To this aim, the present work proposes a calibrationless CS regularized pMRI approach. A Stacked Convolutional Denoising Autoencoder (SCDAE) is used for accurate estimation of the coil-wise sensitivity maps. The present work also uses an interferometry modulated Radio Frequency (RF) coil that not only enhances the resolution in the Field of View (FoV), but also reduces the interference on the adjacent FoVs. Extensive simulation results show that the proposed method enables reconstruction of an MR image with size 256 × 256 from 25% measurements in approximately 0.57 s and offers a performance improvement in Peak-Signal-to-Noise Ratio (PSNR) by 2 ± 0.18 dB and Structural SIMilarity (SSIM) by 0.2 ± 0.06 over the state-of-the-art methods.

Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR).

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the measurements. The main challenge with this strategy is the high computational complexity of matrix completion. We introduce a deep learning (DL) approach to significantly reduce the computational complexity. Specifically, we use a convolutional neural network (CNN)-based filterbank that is trained to estimate the annihilation relations from imperfect (under-sampled and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main reason for the computational efficiency is the pre-learning of the parameters of the non-linear CNN from exemplar data, compared to SLR schemes that learn the linear filterbank parameters from the dataset itself. Experimental comparisons show that the proposed scheme can enable calibration-less parallel MRI; it can offer performance similar to SLR schemes while reducing the runtime by around three orders of magnitude. Unlike pre-calibrated and self-calibrated approaches, the proposed uncalibrated approach is insensitive to motion errors and affords higher acceleration. The proposed scheme also incorporates image domain priors that are complementary, thus significantly improving the performance over that of SLR schemes.

Triple-D network for efficient undersampled magnetic resonance images reconstruction

Compressed sensing (CS) theory can help accelerate magnetic resonance imaging (MRI) by sampling partial k-space measurements. However, conventional optimization-based CS-MRI methods are often time-consuming and are based on fixed transform or shallow image dictionaries, which limits modeling capabilities. Recently, deep learning models have been used to solve the CS-MRI problem. However, recent researches have focused on modeling in image domain, and the potential of k-space modeling capability has not been utilized seriously. In this paper, we propose a deep model called Dual Domain Dense network (Triple-D network), which consisted of some k-space and image domain sub-network. These sub-networks are connected with dense connections, which can utilize feature maps at different levels to enhance performance. To further promote model capabilities, we use two strategies: multi-supervision strategies, which can avoid loss of supervision information; channel-wise attention layer (CA layer), which can adaptively adjust the weight of the feature map. Experimental results show that the proposed Triple-D network provides promising performance in CS-MRI, and it can effectively work on different sampling trajectories and noisy settings.

MRI reconstruction using deep Bayesian estimation.

To develop a deep learning-based Bayesian estimation for MRI reconstruction. We modeled the MRI reconstruction problem with Bayes's theorem, following the recently proposed PixelCNN++ method. The image reconstruction from incomplete k-space measurement was obtained by maximizing the posterior possibility. A generative network was utilized as the image prior, which was computationally tractable, and the k-space data fidelity was enforced by using an equality constraint. The stochastic backpropagation was utilized to calculate the descent gradient in the process of maximum a posterior, and a projected subgradient method was used to impose the equality constraint. In contrast to the other deep learning reconstruction methods, the proposed one used the likelihood of prior as the training loss and the objective function in reconstruction to improve the image quality. The proposed method showed an improved performance in preserving image details and reducing aliasing artifacts, compared with GRAPPA, -ESPRiT, model-based deep learning architecture for inverse problems (MODL), and variational network (VN), last two were state-of-the-art deep learning reconstruction methods. The proposed method generally achieved more than 3 dB peak signal-to-noise ratio improvement for compressed sensing and parallel imaging reconstructions compared with the other methods. The Bayesian estimation significantly improved the reconstruction performance, compared with the conventional -sparsity prior in compressed sensing reconstruction tasks. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.

A deep error correction network for compressed sensing MRI

BackgroundCS-MRI (compressed sensing for magnetic resonance imaging) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. Due to imperfect modelings in the inverse imaging, state-of-the-art CS-MRI methods tend to leave structural reconstruction errors. Compensating such errors in the reconstruction could help further improve the reconstruction quality.ResultsIn this work, we propose a DECN (deep error correction network) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a CNN (convolutional neural network) to map the k-space data in a way that adjusts for the reconstruction error of the template image. We propose a deep error correction network. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.ConclusionsIn the proposed a deep error correction framework, any off-the-shelf CS-MRI algorithm can be used as template generation. Then a deep neural network is used to compensate reconstruction errors. The promising experimental results validate the effectiveness and utility of the proposed framework.

Deep-Learning-Based Optimization of the Under-Sampling Pattern in MRI

In compressed sensing MRI (CS-MRI), k-space measurements are under-sampled to achieve accelerated scan times. CS-MRI presents two fundamental problems: (1) where to sample and (2) how to reconstruct an under-sampled scan. In this article, we tackle both problems simultaneously for the specific case of 2D Cartesian sampling, using a novel end-to-end learning framework that we call LOUPE (Learning-based Optimization of the Under-sampling PattErn). Our method trains a neural network model on a set of full-resolution MRI scans, which are retrospectively under-sampled on a 2D Cartesian grid and forwarded to an anti-aliasing (a.k.a. reconstruction) model that computes a reconstruction, which is in turn compared with the input. This formulation enables a data-driven optimized under-sampling pattern at a given sparsity level. In our experiments, we demonstrate that LOUPE-optimized under-sampling masks are data-dependent, varying significantly with the imaged anatomy, and perform well with different reconstruction methods. We present empirical results obtained with a large-scale, publicly available knee MRI dataset, where LOUPE offered superior reconstruction quality across different conditions. Even with an aggressive 8-fold acceleration rate, LOUPE's reconstructions contained much of the anatomical detail that was missed by alternative masks and reconstruction methods. Our experiments also show how LOUPE yielded optimal under-sampling patterns that were significantly different for brain vs knee MRI scans. Our code is made freely available at https://github.com/cagladbahadir/LOUPE/ .

RARE: Image Reconstruction Using Deep Priors Learned Without Groundtruth

Regularization by denoising (RED) is an image reconstruction framework that uses an image denoiser as a prior. Recent work has shown the state-of-the-art performance of RED with learned denoisers corresponding to pre-trained convolutional neural nets (CNNs). In this work, we propose to broaden the current denoiser-centric view of RED by considering priors corresponding to networks trained for more general artifact-removal. The key benefit of the proposed family of algorithms, called regularization by artifact-removal (RARE), is that it can leverage priors learned on datasets containing only undersampled measurements. This makes RARE applicable to problems where it is practically impossible to have fully-sampled groundtruth data for training. We validate RARE on both simulated and experimentally collected data by reconstructing a free-breathing whole-body 3D MRIs into ten respiratory phases from heavily undersampled k-space measurements. Our results corroborate the potential of learning regularizers for iterative inversion directly on undersampled and noisy measurements.

A divide-and-conquer approach to compressed sensing MRI

Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within the Fourier measurement domain is distributed non-uniformly is often neglected during reconstruction. As a result, more densely sampled low frequency information tends to dominate penalization schemes for reconstructing MRI at the expense of high frequency details. In this paper, we propose a new framework for CS-MRI inversion in which we decompose the observed k-space data into “subspaces” via sets of filters in a lossless way, and reconstruct the images in these various spaces individually using off-the-shelf algorithms. We then fuse the results to obtain the final reconstruction. In this way, we are able to focus reconstruction on frequency information within the entire k-space more equally, preserving both high and low frequency details. We demonstrate that the proposed framework is competitive with state-of-the-art methods in CS-MRI in terms of quantitative performance, and often improves an algorithm's results qualitatively compared with its direct application to k-space.

Accelerated Dynamic MRI Using Kernel-Based Low Rank Constraint

We present a novel reconstruction method for dynamic MR images from highly under-sampled k-space measurements. The reconstruction problem is posed as spectrally regularized matrix recovery problem, where kernel-based low rank constraint is employed to effectively utilize the non-linear correlations between the images in the dynamic sequence. Unlike other kernel-based methods, we use a single-step regularized reconstruction approach to simultaneously learn the kernel basis functions and the weights. The objective function is optimized using variable splitting and alternating direction method of multipliers. The framework can seamlessly handle additional sparsity constraints such as spatio-temporal total variation. The algorithm performance is evaluated on a numerical phantom and in vivo data sets and it shows significant improvement over the comparison methods.