Reconstruction of 3D dynamic contrast-enhanced magnetic resonance imaging using nonlocal means

Enhancement-constrained acceleration: A robust reconstruction framework in breast DCE-MRI

In patients with dense breasts or at high risk of breast cancer, dynamic contrast enhanced MRI (DCE-MRI) is a highly sensitive diagnostic tool. However, its specificity is highly variable and sometimes low; quantitative measurements of contrast uptake parameters may improve specificity and mitigate this issue. To improve diagnostic accuracy, data need to be captured at high spatial and temporal resolution. While many methods exist to accelerate MRI temporal resolution, not all are optimized to capture breast DCE-MRI dynamics. We propose a novel, flexible, and powerful framework for the reconstruction of highly-undersampled DCE-MRI data: enhancement-constrained acceleration (ECA). Enhancement-constrained acceleration uses an assumption of smooth enhancement at small time-scale to estimate points of smooth enhancement curves in small time intervals at each voxel. This method is tested in silico with physiologically realistic virtual phantoms, simulating state-of-the-art ultrafast acquisitions at 3.5s temporal resolution reconstructed at 0.25s temporal resolution (demo code available here). Virtual phantoms were developed from real patient data and parametrized in continuous time with arterial input function (AIF) models and lesion enhancement functions. Enhancement-constrained acceleration was compared to standard ultrafast reconstruction in estimating the bolus arrival time and initial slope of enhancement from reconstructed images. We found that the ECA method reconstructed images at 0.25s temporal resolution with no significant loss in image fidelity, a 4x reduction in the error of bolus arrival time estimation in lesions (p < 0.01) and 11x error reduction in blood vessels (p < 0.01). Our results suggest that ECA is a powerful and versatile tool for breast DCE-MRI.

Qualitative and Quantitative Assessment of Nonlocal Means Reconstruction Algorithm in a Flexible PET Scanner

OBJECTIVE. Flexible PET (fxPET) was designed to fit existing MRI systems. The newly modified nonlocal means (NLM) algorithm is combined with the 3D dynamic row-action maximum likelihood algorithm (DRAMA). We investigated qualitative and quantitative acceptability of fxPET images reconstructed by modified NLM compared with whole-body (WB) PET/CT images and conventional 3D DRAMA reconstruction alone. MATERIALS AND METHODS. Fifty-nine patients with known or suspected malignancies underwent WB PET/CT scanning approximately 1 hour after the injection of ¹⁸F-FDG, after which they underwent fxPET scanning. Two readers rated the quality of fxPET images by consensus. Detection rate (the proportion of lesions found on PET), maximal standardized uptake value (SUV_max), metabolic tumor volume (MTV), total lesion glycolysis (TLG), tumor-to-normal liver ratio (TNR), and background liver signal-to-noise ratio (SNR) were compared among the three datasets. RESULTS. Higher image quality was obtained by modified NLM reconstruction than by conventional reconstruction without statistical significance. The detection rate was comparable among three datasets. SUV_max was significantly higher, and MTV and TLG were significantly lower in the modified NLM dataset (p < 0.002) than in the other two datasets, with significantly positive correlations (p < 0.001; Spearman rank correlation coefficient, 0.87-0.99). The TNRs in modified NLM images were significantly larger than in the other datasets (p < 0.05). The background SNRs in modified NLM images were comparable with those in WB PET/CT images, and significantly higher than in the conventional fxPET images (p < 0.005). CONCLUSION. The modified NLM algorithm was clinically acceptable, yielding higher TNR and background SNR compared with conventional reconstruction. Image quality and the lesion detection rate were comparable in this population.

Image Denoising Using Non-Local Means (NLM) Approach in Magnetic Resonance (MR) Imaging: A Systematic Review

The non-local means (NLM) noise reduction algorithm is well known as an excellent technique for removing noise from a magnetic resonance (MR) image to improve the diagnostic accuracy. In this study, we undertook a systematic review to determine the effectiveness of the NLM noise reduction algorithm in MR imaging. A systematic literature search was conducted of three databases of publications dating from January 2000 to March 2020; of the 82 publications reviewed, 25 were included in this study. The subjects were categorized into four major frameworks and analyzed for each research result. Research in NLM noise reduction for MR images has been increasing worldwide; however, it was found to have slightly decreased since 2016. It was found that the NLM technique was most frequently used on brain images taken using the general MR imaging technique; these were most frequently performed during simultaneous real and simulated experimental studies. In particular, comparison parameters were frequently used to evaluate the effectiveness of the algorithm on MR images. The ultimate goal is to provide an accurate method for the diagnosis of disease, and our conclusion is that the NLM noise reduction algorithm is a promising method of achieving this goal.

Iterative PET Image Reconstruction Using Convolutional Neural Network Representation

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently, the deep neural networks have been widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this paper, we trained a deep residual convolutional neural network to improve PET image quality by using the existing inter-patient information. An innovative feature of the proposed method is that we embed the neural network in the iterative reconstruction framework for image representation, rather than using it as a post-processing tool. We formulate the objective function as a constrained optimization problem and solve it using the alternating direction method of multipliers algorithm. Both simulation data and hybrid real data are used to evaluate the proposed method. Quantification results show that our proposed iterative neural network method can outperform the neural network denoising and conventional penalized maximum likelihood methods.

MULTI-ENERGY CONE-BEAM CT RECONSTRUCTION WITH A SPATIAL SPECTRAL NONLOCAL MEANS ALGORITHM

Multi-energy computed tomography (CT) is an emerging medical image modality with a number of potential applications in diagnosis and therapy. However, high system cost and technical barriers obstruct its step into routine clinical practice. In this study, we propose a framework to realize multi-energy cone beam CT (ME-CBCT) on the CBCT system that is widely available and has been routinely used for radiotherapy image guidance. In our method, a kVp switching technique is realized, which acquires x-ray projections with kVp levels cycling through a number of values. For this kVp-switching based ME-CBCT acquisition, x-ray projections of each energy channel are only a subset of all the acquired projections. This leads to an undersampling issue, posing challenges to the reconstruction problem. We propose a spatial spectral non-local means (ssNLM) method to reconstruct ME-CBCT, which employs image correlations along both spatial and spectral directions to suppress noisy and streak artifacts. To address the intensity scale difference at different energy channels, a histogram matching method is incorporated. Our method is different from conventionally used NLM methods in that spectral dimension is included, which helps to effectively remove streak artifacts appearing at different directions in images with different energy channels. Convergence analysis of our algorithm is provided. A comprehensive set of simulation and real experimental studies demonstrate feasibility of our ME-CBCT scheme and the capability of achieving superior image quality compared to conventional filtered backprojection-type (FBP) and NLM reconstruction methods.

Dynamic field-of-view imaging to increase temporal resolution in the early phase of contrast media uptake in breast DCE-MRI: A feasibility study

PURPOSE

To increase diagnostic accuracy of breast MRI by increasing temporal resolution and more accurately sampling the early kinetics of contrast media uptake. We tested the feasibility of accelerating bilateral breast DCE-MRI by reducing the FOV, allowing aliasing, and unfolding the resulting images.

METHODS

Previous experience with an "ultrafast" protocol for bilateral breast DCE-MRI (6-10 s temporal resolution) showed that the number of significantly enhancing voxels is very low in the first 30-45 s after contrast media injection. This suggests that overlap of enhancing voxels in aliased images will be very infrequent. Therefore, aliased images can be acquired during the first 30-45 s after contrast media injection and unfolded to produce full-FOV images with few errors. In a proof-of-principle test, aliased images were simulated from the first 30 s of full-FOV acquisitions. Cases with relatively dense early enhancement were selected to test this method in a worst-case scenario. In an initial test, an FOV of 60% the size of the full FOV was simulated. To reduce the probability of errors due to overlapping voxels in aliased images, we then tested a dynamic FOV approach. The FOV was progressively increased so that enhancing voxels could not overlap at multiple time-points, and areas where enhancing voxels overlapped at a given time-point could be unfolded by interpolating between the preceding and subsequent time-points (acquired with different FOVs). The simulated FOV sizes for each of the time-points were 31%, 44%, and 77% of the full FOV. Subtraction images (post- minus precontrast) were generated for aliased images and filtered to select significantly enhancing voxels. Comparison of early, highly aliased images, with later, less aliased images then helped to identify the true locations of enhancing voxels.

RESULTS

In the initial aliasing simulations, an average of 2.9% of the enhancing voxels above the chest wall overlapped in the aliased images (range 0.1%-6.7%). The similarity between simulated unfolded images and the correct full-FOV images, evaluated using CW-SSIM (complex wavelet similarity index), was 0.50 ± 0.26, 0.76 ± 0.09, and 0.80 ± 0.10 for the first, second, and third time-point, respectively (numbers closer to 1 indicate more similar images). For the dynamic FOV tests, an average of 11% of the enhancing voxels above the chest wall overlapped (range 0%-40%) due to greater aliasing at early time-points. Despite more voxels overlapping, the CW-SSIM values for the data acquired with dynamic FOVs were 0.64 ± 0.25, 0.93 ± 0.04, and 0.97 ± 0.02 for the first, second, and third time-points, respectively.

CONCLUSIONS

Dynamic FOV imaging allows accelerated bilateral breast DCE-MRI during the early contrast media uptake phase. This method relies on the sparsity of enhancement at the early phases of DCE-MRI of the breast. The results of simulations suggest that dynamic FOV imaging and unfolding produces images that are very close to fully sampled images, and allows temporal resolution as high as 2 s per image.

Feasibility of high spatiotemporal resolution for an abbreviated 3D radial breast MRI protocol

PURPOSE

To develop a volumetric imaging technique with 0.8-mm isotropic resolution and 10-s/volume rate to detect and analyze breast lesions in a bilateral, dynamic, contrast-enhanced MRI exam.

METHODS

A local low-rank temporal reconstruction approach that also uses parallel imaging and spatial compressed sensing was designed to create rapid volumetric frame rates during a contrast-enhanced breast exam (vastly undersampled isotropic projection [VIPR] spatial compressed sensing with temporal local low-rank [STELLR]). The dynamic-enhanced data are subtracted in k-space from static mask data to increase sparsity for the local low-rank approach to maximize temporal resolution. A T₁ -weighted 3D radial trajectory (VIPR iterative decomposition with echo asymmetry and least squares estimation [IDEAL]) was modified to meet the data acquisition requirements of the STELLR approach. Additionally, the unsubtracted enhanced data are reconstructed using compressed sensing and IDEAL to provide high-resolution fat/water separation. The feasibility of the approach and the dual reconstruction methodology is demonstrated using a 16-channel breast coil and a 3T MR scanner in 6 patients.

RESULTS

The STELLR temporal performance of subtracted data matched the expected temporal perfusion enhancement pattern in small and large vascular structures. Differential enhancement within heterogeneous lesions is demonstrated with corroboration from a basic reconstruction using a strict 10-second temporal footprint. Rapid acquisition, reliable fat suppression, and high spatiotemporal resolution are presented, despite significant data undersampling.

CONCLUSION

The STELLR reconstruction approach of 3D radial sampling with mask subtraction provides a high-performance imaging technique for characterizing enhancing structures within the breast. It is capable of maintaining temporal fidelity, while visualizing breast lesions with high detail over a large FOV to include both breasts.

Applications of nonlocal means algorithm in low-dose X-ray CT image processing and reconstruction: A review

Low-dose X-ray computed tomography (LDCT) imaging is highly recommended for use in the clinic because of growing concerns over excessive radiation exposure. However, the CT images reconstructed by the conventional filtered back-projection (FBP) method from low-dose acquisitions may be severely degraded with noise and streak artifacts due to excessive X-ray quantum noise, or with view-aliasing artifacts due to insufficient angular sampling. In 2005, the nonlocal means (NLM) algorithm was introduced as a non-iterative edge-preserving filter to denoise natural images corrupted by additive Gaussian noise, and showed superior performance. It has since been adapted and applied to many other image types and various inverse problems. This paper specifically reviews the applications of the NLM algorithm in LDCT image processing and reconstruction, and explicitly demonstrates its improving effects on the reconstructed CT image quality from low-dose acquisitions. The effectiveness of these applications on LDCT and their relative performance are described in detail.

Sparse Reconstruction Techniques in Magnetic Resonance Imaging: Methods, Applications, and Challenges to Clinical Adoption

The family of sparse reconstruction techniques, including the recently introduced compressed sensing framework, has been extensively explored to reduce scan times in magnetic resonance imaging (MRI). While there are many different methods that fall under the general umbrella of sparse reconstructions, they all rely on the idea that a priori information about the sparsity of MR images can be used to reconstruct full images from undersampled data. This review describes the basic ideas behind sparse reconstruction techniques, how they could be applied to improve MRI, and the open challenges to their general adoption in a clinical setting. The fundamental principles underlying different classes of sparse reconstructions techniques are examined, and the requirements that each make on the undersampled data outlined. Applications that could potentially benefit from the accelerations that sparse reconstructions could provide are described, and clinical studies using sparse reconstructions reviewed. Lastly, technical and clinical challenges to widespread implementation of sparse reconstruction techniques, including optimization, reconstruction times, artifact appearance, and comparison with current gold standards, are discussed.

3D Cartesian MRI with compressed sensing and variable view sharing using complementary poisson-disc sampling

PURPOSE

To enable robust, high spatio-temporal-resolution three-dimensional Cartesian MRI using a scheme incorporating a novel variable density random k-space sampling trajectory allowing flexible and retrospective selection of the temporal footprint with compressed sensing (CS).

METHODS

A complementary Poisson-disc k-space sampling trajectory was designed to allow view sharing and varying combinations of reduced view sharing with CS from the same prospective acquisition. These schemes were used for two-point Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) of the breast and abdomen. Results were validated in vivo with a novel approach using variable-flip-angle data, which was retrospectively accelerated using the same methods but offered a ground truth.

RESULTS

In breast DCE-MRI, the temporal footprint could be reduced 2.3-fold retrospectively without introducing noticeable artifacts, improving depiction of rapidly enhancing lesions. Further, experiments with variable-flip-angle data showed that reducing view sharing improved accuracy in reconstruction and T₁ mapping. In abdominal MRI, 2.3-fold and 3.6-fold reductions in temporal footprint allowed reduced motion artifacts.

CONCLUSION

The complementary-Poisson-disc k-space sampling trajectory allowed a retrospective spatiotemporal resolution tradeoff using CS and view sharing, imparting robustness to motion and contrast enhancement. The technique was also validated using a novel approach of fully acquired variable-flip-angle acquisition. Magn Reson Med 77:1774-1785, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

An Extended Bayesian-FBP Algorithm

Recently we developed a Bayesian-FBP (Filtered Backprojection) algorithm for CT image reconstruction. This algorithm is also referred to as the FBP-MAP (FBP Maximum a Posteriori) algorithm. This non-iterative Bayesian algorithm has been applied to real-time MRI, in which the k-space is under-sampled. This current paper investigates the possibility to extend this Bayesian-FBP algorithm by introducing more controlling parameters. Thus, our original Bayesian-FBP algorithm became a special case of the extended Bayesian-FBP algorithm. A cardiac patient data set is used in this paper to evaluate the extended Bayesian-FBP algorithm, and the result from a well-establish iterative algorithm with L₁-norms is used as the gold standard. If the parameters are selected properly, the extended Bayesian-FBP algorithm can outperform the original Bayesian-FBP algorithm.

Highly accelerated dynamic contrast enhanced imaging

PURPOSE

Dynamic contrast-enhanced imaging provides unique physiological information, notably the endothelial permeability (K(trans)), and may improve the diagnosis and management of multiple pathologies. Current acquisition methods provide limited spatial-temporal resolution and field-of-view, often preventing characterization of the entire pathology and precluding measurement of the arterial input function. We present a method for highly accelerated dynamic imaging and demonstrate its utility for dynamic contrast-enhanced modeling.

METHODS

We propose a novel Poisson ellipsoid sampling scheme and enforce multiple spatial and temporal l1-norm constraints during image reconstruction. Retrospective and prospective analyses were performed to validate the approach.

RESULTS

Retrospectively, no mean bias or diverging trend was observed as the acceleration rate was increased from 3× to 18×; less than 10% error was measured in K(trans) at any individual rates in this range. Prospectively accelerated images at a rate of 36× enabled full brain coverage with 0.94 × 0.94 × 1.9 mm(3) spatial and 4.1 s temporal resolutions. Images showed no visible degradation and provided accurate K(trans) values when compared to a clinical population.

CONCLUSION

Highly accelerated dynamic MRI using compressed sensing and parallel imaging provides accurate permeability modeling and enables full brain, high resolution acquisitions.

Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain

Background

Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most state-of-the-art reconstruction models seldom consider composite regularization upon the various structural features of images and transform coefficients sub-bands. Therefore, these two points lead to high sampling rates for reconstructing high-quality images.

Methods

In this paper, an efficient composite sparsity structure is proposed. It learns adaptive dictionary from lowpass uniform discrete curvelet transform sub-band coefficients patches. Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data. It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l₁ sparse regularization and constraining k-space measurements fidelity. A new augmented Lagrangian method is then introduced to optimize the reconstruction model. It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.

Results

Experimental results on in vivo data show that the proposed method obtains high-quality reconstructed images. The reconstructed images exhibit the least aliasing artifacts and reconstruction error among current CS MRI methods.

Conclusions

The proposed sparsity structure can fit and provide hierarchical sparsity for magnetic resonance images simultaneously, bridging the gap between predefined sparse representation methods and explicit dictionary. The new augmented Lagrangian method provides solutions fully complying to the composite regularization reconstruction model with fast convergence speed.

Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI

Compressed sensing MRI (CS-MRI) is a promising technology to accelerate magnetic resonance imaging. Both improving the image quality and reducing the computation time are important for this technology. Recently, a patch-based directional wavelet (PBDW) has been applied in CS-MRI to improve edge reconstruction. However, this method is time consuming since it involves extensive computations, including geometric direction estimation and numerous iterations of wavelet transform. To accelerate computations of PBDW, we propose a general parallelization of patch-based processing by taking the advantage of multicore processors. Additionally, two pertinent optimizations, excluding smooth patches and pre-arranged insertion sort, that make use of sparsity in MR images are also proposed. Simulation results demonstrate that the acceleration factor with the parallel architecture of PBDW approaches the number of central processing unit cores, and that pertinent optimizations are also effective to make further accelerations. The proposed approaches allow compressed sensing MRI reconstruction to be accomplished within several seconds.

Parallel computing of patch-based nonlocal operator and its application in compressed sensing MRI

Magnetic resonance imaging has been benefited from compressed sensing in improving imaging speed. But the computation time of compressed sensing magnetic resonance imaging (CS-MRI) is relatively long due to its iterative reconstruction process. Recently, a patch-based nonlocal operator (PANO) has been applied in CS-MRI to significantly reduce the reconstruction error by making use of self-similarity in images. But the two major steps in PANO, learning similarities and performing 3D wavelet transform, require extensive computations. In this paper, a parallel architecture based on multicore processors is proposed to accelerate computations of PANO. Simulation results demonstrate that the acceleration factor approaches the number of CPU cores and overall PANO-based CS-MRI reconstruction can be accomplished in several seconds.

Algebraic reconstruction technique for parallel imaging reconstruction of undersampled radial data: application to cardiac cine

PURPOSE

To investigate algebraic reconstruction technique (ART) for parallel imaging reconstruction of radial data, applied to accelerated cardiac cine.

METHODS

A graphics processing unit (GPU)-accelerated ART reconstruction was implemented and applied to simulations, point spread functions and in 12 subjects imaged with radial cardiac cine acquisitions. Cine images were reconstructed with radial ART at multiple undersampling levels (192 Nr × Np  = 96 to 16). Images were qualitatively and quantitatively analyzed for sharpness and artifacts, and compared to filtered back-projection, and conjugate gradient SENSE.

RESULTS

Radial ART provided reduced artifacts and mainly preserved spatial resolution, for both simulations and in vivo data. Artifacts were qualitatively and quantitatively less with ART than filtered back-projection using 48, 32, and 24 Np , although filtered back-projection provided quantitatively sharper images at undersampling levels of 48-24 Np (all P < 0.05). Use of undersampled radial data for generating auto-calibrated coil-sensitivity profiles resulted in slightly reduced quality. ART was comparable to conjugate gradient SENSE. GPU-acceleration increased ART reconstruction speed 15-fold, with little impact on the images.

CONCLUSION

GPU-accelerated ART is an alternative approach to image reconstruction for parallel radial MR imaging, providing reduced artifacts while mainly maintaining sharpness compared to filtered back-projection, as shown by its first application in cardiac studies.

Potential of compressed sensing in quantitative MR imaging of cancer

Classic signal processing theory dictates that, in order to faithfully reconstruct a band-limited signal (e.g., an image), the sampling rate must be at least twice the maximum frequency contained within the signal, i.e., the Nyquist frequency. Recent developments in applied mathematics, however, have shown that it is often possible to reconstruct signals sampled below the Nyquist rate. This new method of compressed sensing (CS) requires that the signal have a concise and extremely dense representation in some mathematical basis. Magnetic resonance imaging (MRI) is particularly well suited for CS approaches, owing to the flexibility of data collection in the spatial frequency (Fourier) domain available in most MRI protocols. With custom CS acquisition and reconstruction strategies, one can quickly obtain a small subset of the full data and then iteratively reconstruct images that are consistent with the acquired data and sparse by some measure. Successful use of CS results in a substantial decrease in the time required to collect an individual image. This extra time can then be harnessed to increase spatial resolution, temporal resolution, signal-to-noise, or any combination of the three. In this article, we first review the salient features of CS theory and then discuss the specific barriers confronting CS before it can be readily incorporated into clinical quantitative MRI studies of cancer. We finally illustrate applications of the technique by describing examples of CS in dynamic contrast-enhanced MRI and dynamic susceptibility contrast MRI.

Incorporating anatomical side information into PET reconstruction using nonlocal regularization

With the introduction of combined positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI) scanners, there is an increasing emphasis on reconstructing PET images with the aid of the anatomical side information obtained from X-ray CT or MRI scanners. In this paper, we propose a new approach to incorporating prior anatomical information into PET reconstruction using the nonlocal regularization method. The nonlocal regularizer developed for this application is designed to selectively consider the anatomical information only when it is reliable. As our proposed nonlocal regularization method does not directly use anatomical edges or boundaries which are often used in conventional methods, it is not only free from additional processes to extract anatomical boundaries or segmented regions, but also more robust to the signal mismatch problem that is caused by the indirect relationship between the PET image and the anatomical image. We perform simulations with digital phantoms. According to our experimental results, compared to the conventional method based on the traditional local regularization method, our nonlocal regularization method performs well even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

Nonlocal regularization of inverse problems: a unified variational framework

We introduce a unifying energy minimization framework for nonlocal regularization of inverse problems. In contrast to the weighted sum of square differences between image pixels used by current schemes, the proposed functional is an unweighted sum of inter-patch distances. We use robust distance metrics that promote the averaging of similar patches, while discouraging the averaging of dissimilar patches. We show that the first iteration of a majorize-minimize algorithm to minimize the proposed cost function is similar to current nonlocal methods. The reformulation thus provides a theoretical justification for the heuristic approach of iterating nonlocal schemes, which re-estimate the weights from the current image estimate. Thanks to the reformulation, we now understand that the widely reported alias amplification associated with iterative nonlocal methods are caused by the convergence to local minimum of the nonconvex penalty. We introduce an efficient continuation strategy to overcome this problem. The similarity of the proposed criterion to widely used nonquadratic penalties (e.g., total variation and lp semi-norms) opens the door to the adaptation of fast algorithms developed in the context of compressive sensing; we introduce several novel algorithms to solve the proposed nonlocal optimization problem. Thanks to the unifying framework, these fast algorithms are readily applicable for a large class of distance metrics.

High spatial and temporal resolution dynamic contrast-enhanced magnetic resonance angiography using compressed sensing with magnitude image subtraction

PURPOSE

We propose a compressed-sensing (CS) technique based on magnitude image subtraction for high spatial and temporal resolution dynamic contrast-enhanced MR angiography (CE-MRA).

METHODS

Our technique integrates the magnitude difference image into the CS reconstruction to promote subtraction sparsity. Fully sampled Cartesian 3D CE-MRA datasets from 6 volunteers were retrospectively under-sampled and three reconstruction strategies were evaluated: k-space subtraction CS, independent CS, and magnitude subtraction CS. The techniques were compared in image quality (vessel delineation, image artifacts, and noise) and image reconstruction error. Our CS technique was further tested on seven volunteers using a prospectively under-sampled CE-MRA sequence.

RESULTS

Compared with k-space subtraction and independent CS, our magnitude subtraction CS provides significantly better vessel delineation and less noise at 4× acceleration, and significantly less reconstruction error at 4× and 8× (P < 0.05 for all). On a 1-4 point image quality scale in vessel delineation, our technique scored 3.8 ± 0.4 at 4×, 2.8 ± 0.4 at 8×, and 2.3 ± 0.6 at 12× acceleration. Using our CS sequence at 12× acceleration, we were able to acquire dynamic CE-MRA with higher spatial and temporal resolution than current clinical TWIST protocol while maintaining comparable image quality (2.8 ± 0.5 vs. 3.0 ± 0.4, P = NS).

CONCLUSION

Our technique is promising for dynamic CE-MRA.

Non-Iterative Reconstruction with a Prior for Undersampled Radial MRI Data

This paper develops an FBP-MAP (Filtered Backprojection, Maximum a Posteriori) algorithm to reconstruct MRI images from under-sampled data. An objective function is first set up for the MRI reconstruction problem with a data fidelity term and a Bayesian term. The Bayesian term is a constraint in the temporal dimension. This objective function is minimized using the calculus of variations. The proposed algorithm is non-iterative. Undersampled dynamic myocardial perfusion MRI data were used to test the feasibility of the proposed technique. It is shown that the non-iterative Fourier reconstruction method effectively incorporates the temporal constraint and significantly reduces the angular aliasing artifacts caused by undersampling. A significant advantage of the proposed non-iterative Fourier technique over the iterative techniques is its fast computation time.

Penalized likelihood PET image reconstruction using patch-based edge-preserving regularization

Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels. The most commonly used quadratic penalty often oversmoothes edges and fine features in reconstructed images. Nonquadratic penalties can preserve edges but often introduce piece-wise constant blocky artifacts and the results are also sensitive to the hyper-parameter that controls the shape of the penalty function. This paper presents a patch-based regularization for iterative image reconstruction that uses neighborhood patches instead of individual pixels in computing the nonquadratic penalty. The new regularization is more robust than the conventional pixel-based regularization in differentiating sharp edges from random fluctuations due to noise. An optimization transfer algorithm is developed for the penalized maximum likelihood estimation. Each iteration of the algorithm can be implemented in three simple steps: an EM-like image update, an image smoothing and a pixel-by-pixel image fusion. Computer simulations show that the proposed patch-based regularization can achieve higher contrast recovery for small objects without increasing background variation compared with the quadratic regularization. The reconstruction is also more robust to the hyper-parameter than conventional pixel-based nonquadratic regularizations. The proposed regularization method has been applied to real 3-D PET data.

Temporal/spatial resolution improvement of in vivo DCE-MRI with compressed sensing-optimized FLASH

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides critical information regarding tumor perfusion and permeability by injecting a T(1) contrast agent, such as Gd-DTPA, and making a time-resolved measurement of signal increase. Both temporal and spatial resolutions are required to be high to achieve an accurate and reproducible estimation of tumor perfusion. However, the dynamic nature of the DCE experiment limits simultaneous improvement of temporal and spatial resolution by conventional methods. Compressed sensing (CS) has become an important tool for the acceleration of imaging times in MRI, which is achieved by enabling the reconstruction of subsampled data. Similarly, CS algorithms can be utilized to improve the temporal/spatial resolution of DCE-MRI, and several works describing retrospective simulations have demonstrated the feasibility of such improvements. In this study, the fast low angle shot sequence was modified to implement a Cartesian, CS-optimized, sub-Nyquist phase encoding acquisition/reconstruction with multiple two-dimensional slice selections and was tested on water phantoms and animal tumor models. The mean voxel-level concordance correlation coefficient for Ak(ep) values obtained from ×4 and ×8 accelerated and the fully sampled data was 0.87±0.11 and 0.83±0.11, respectively (n=6), with optimized CS parameters. In this case, the reduction of phase encoding steps made possible by CS reconstruction improved effectively the temporal/spatial resolution of DCE-MRI data using an in vivo animal tumor model (n=6) and may be useful for the investigation of accelerated acquisitions in preclinical and clinical DCE-MRI trials.

Group sparse reconstruction using intensity-based clustering

Compressed sensing has been of great interest to speed up the acquisition of MR images. The k-t group sparse (k-t GS) method has recently been introduced for dynamic MR images to exploit not just the sparsity, as in compressed sensing, but also the spatial group structure in the sparse representation. k-t GS achieves higher acceleration factors compared to the conventional compressed sensing method. However, it assumes a spatial structure in the sparse representation and it requires a time consuming hard-thresholding reconstruction scheme. In this work, we propose to modify k-t GS by incorporating prior information about the sorted intensity of the signal in the sparse representation, for a more general and robust group assignment. This approach is referred to as group sparse reconstruction using intensity-based clustering. The feasibility of the proposed method is demonstrated for static 3D hyperpolarized lung images and applications with both dynamic and intensity changes, such as 2D cine and perfusion cardiac MRI, with retrospective undersampling. For all reported acceleration factors the proposed method outperforms the original compressed sensing method. Improved reconstruction over k-t GS method is demonstrated when k-t GS assumptions are not satisfied. The proposed method was also applied to cardiac cine images with a prospective sevenfold acceleration, outperforming the standard compressed sensing reconstruction.

Fast 3D contrast enhanced MRI of the liver using temporal resolution acceleration with constrained evolution reconstruction

Time-resolved imaging is crucial for the accurate diagnosis of liver lesions. Current contrast enhanced liver magnetic resonance imaging acquires a few phases in sequential breath-holds. The image quality is susceptible to bolus timing errors, which could result in missing the critical arterial phase. This impairs the detection of malignant tumors that are supplied primarily by the hepatic artery. In addition, the temporal resolution may be too low to reliably separate the arterial phase from the portal venous phase. In this study, a method called temporal resolution acceleration with constrained evolution reconstruction was developed with three-dimensional volume coverage and high-temporal frame rate. Data is acquired using a stack of spirals sampling trajectory combined with a golden ratio view order using an eight-channel coil array. Temporal frames are reconstructed from vastly undersampled data sets using a nonlinear inverse algorithm assuming that the temporal changes are small at short time intervals. Numerical and phantom experimental validation is presented. Preliminary in vivo results demonstrated high spatial resolution dynamic three-dimensional images of the whole liver with high frame rates, from which numerous subarterial phases could be easily identified retrospectively.