Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage

Learning Robust and Sparse Principal Components With the α-Divergence

In this paper, novel robust principal component analysis (RPCA) methods are proposed to exploit the local structure of datasets. The proposed methods are derived by minimizing the α -divergence between the sample distribution and the Gaussian density model. The α- divergence is used in different frameworks to represent variants of RPCA approaches including orthogonal, non-orthogonal, and sparse methods. We show that the classical PCA is a special case of our proposed methods where the α- divergence is reduced to the Kullback-Leibler (KL) divergence. It is shown in simulations that the proposed approaches recover the underlying principal components (PCs) by down-weighting the importance of structured and unstructured outliers. Furthermore, using simulated data, it is shown that the proposed methods can be applied to fMRI signal recovery and Foreground-Background (FB) separation in video analysis. Results on real world problems of FB separation as well as image reconstruction are also provided.

Enhanced clinical task-based fMRI metrics through locally low-rank denoising of complex-valued data

OBJECTIVE

This study investigates a locally low-rank (LLR) denoising algorithm applied to source images from a clinical task-based functional MRI (fMRI) exam before post-processing for improving statistical confidence of task-based activation maps.

METHODS

Task-based motor and language fMRI was obtained in eleven healthy volunteers under an IRB approved protocol. LLR denoising was then applied to raw complex-valued image data before fMRI processing. Activation maps generated from conventional non-denoised (control) data were compared with maps derived from LLR-denoised image data. Four board-certified neuroradiologists completed consensus assessment of activation maps; region-specific and aggregate motor and language consensus thresholds were then compared with nonparametric statistical tests. Additional evaluation included retrospective truncation of exam data without and with LLR denoising; a ROI-based analysis tracked t-statistics and temporal SNR (tSNR) as scan durations decreased. A test-retest assessment was performed; retest data were matched with initial test data and compared for one subject.

RESULTS

fMRI activation maps generated from LLR-denoised data predominantly exhibited statistically significant (p = 4.88×10-4 to p = 0.042; one p = 0.062) increases in consensus t-statistic thresholds for motor and language activation maps. Following data truncation, LLR data showed task-specific increases in t-statistics and tSNR respectively exceeding 20 and 50% compared to control. LLR denoising enabled truncation of exam durations while preserving cluster volumes at fixed thresholds. Test-retest showed variable activation with LLR data thresholded higher in matching initial test data.

CONCLUSION

LLR denoising affords robust increases in t-statistics on fMRI activation maps compared to routine processing, and offers potential for reduced scan duration while preserving map quality.

Highlight removal for endoscopic images based on accelerated adaptive non-convex RPCA decomposition

OBJECTIVE

Highlights always occur in endoscopic images due to their special imaging environment. It not only increases the difficulty of observation and diagnosis from surgeons, but also influences the performance of Mixed/Augmented Reality techniques in surgery navigation.

METHODS

In this paper, we propose a novel accelerated adaptive non-convex robust principal component analysis method (AANC-RPCA) to remove highlights in endoscopic images. We first detect absolute highlight pixels of the enhanced endoscopic images with adaptive threshold segmentation. The quasi-convex function is proposed to approximate a new non-convex objective function. With detected highlight pixels and quasi-convex function, it introduces gradient to shrink sparse matrix and obtains a faster speed of convergence. Then we divide the image into multiple blocks and perform the parallel computation to enhance the efficiency. Finally, we design a weighted template that decays outward with dilation and linear filtering to reconstruct the endoscopic images. Our approach is almost independent of hyper-parameters and can achieve adaptive decomposition.

RESULTS

It has been verified on multiple types of endoscopic images through experiments and clinical blind tests. The results demonstrate that our method can obtain the best performance for the recovered images with more details in a shorter time (about 3-5 times).

CONCLUSION

Coupled with the user study, both the quantitative and qualitative results indicate that our approach has the potential to be highly useful in endoscopy images. Compared with the existing highlight removal approaches, our method obtains the SOTA results and has the potential to be applied in the various medical processing processes.

TL-HARDI: Transform learning based accelerated reconstruction of HARDI data

Diffusion magnetic resonance imaging (dMRI) is being extensively used to study the neural architecture of the brain. High angular resolution diffusion imaging (HARDI), a variant of diffusion MRI, measures the diffusion of water molecules along the angular gradient directions in the q-space. It provides better estimates of fiber orientations compared to the traditionally used diffusion tensor imaging (DTI). However, HARDI requires acquisition of relatively large number of samples leading to longer scanning times. Several approaches based on compressive sensing (CS) have been proposed to accelerate HARDI acquisition, leveraging on the sparse representation of the HARDI signal in a pre-specified sparsifying basis. In this paper, we propose to carry out reconstruction of compressively sensed HARDI data using an adaptively learned transform. The transform is learned (i) from the compressive measurements on-the-fly, thereby, eliminating the overhead of choosing fixed sparsifying transforms, and (ii) on overlapping patches of the data, thereby, capturing local image structure effectively. Experiments are conducted on multiple real HARDI data for varying sampling ratios and sampling schemes. The performance of the proposed "TL-HARDI" method is compared with the state-of-the-art methods on various known image quality metrics as well as on dMRI feature maps derived from the reconstructed images. The proposed method is observed to yield better reconstruction than the existing state-of-the-art methods in both quantitative and qualitative comparisons.

Subspace-constrained approaches to low-rank fMRI acceleration

Acceleration methods in fMRI aim to reconstruct high fidelity images from under-sampled k-space, allowing fMRI datasets to achieve higher temporal resolution, reduced physiological noise aliasing, and increased statistical degrees of freedom. While low levels of acceleration are typically part of standard fMRI protocols through parallel imaging, there exists the potential for approaches that allow much greater acceleration. One such existing approach is k-t FASTER, which exploits the inherent low-rank nature of fMRI. In this paper, we present a reformulated version of k-t FASTER which includes additional L2 constraints within a low-rank framework.

We evaluated the effect of three different constraints against existing low-rank approaches to fMRI reconstruction: Tikhonov constraints, low-resolution priors, and temporal subspace smoothness. The different approaches are separately tested for robustness to under-sampling and thermal noise levels, in both retrospectively and prospectively-undersampled finger-tapping task fMRI data. Reconstruction quality is evaluated by accurate reconstruction of low-rank subspaces and activation maps.

The use of L2 constraints was found to achieve consistently improved results, producing high fidelity reconstructions of statistical parameter maps at higher acceleration factors and lower SNR values than existing methods, but at a cost of longer computation time. In particular, the Tikhonov constraint proved very robust across all tested datasets, and the temporal subspace smoothness constraint provided the best reconstruction scores in the prospectively-undersampled dataset. These results demonstrate that regularized low-rank reconstruction of fMRI data can recover functional information at high acceleration factors without the use of any model-based spatial constraints.

Improved statistical efficiency of simultaneous multi-slice fMRI by reconstruction with spatially adaptive temporal smoothing

We introduce an approach to reconstruction of simultaneous multi-slice (SMS)-fMRI data that improves statistical efficiency. The method incorporates regularization to adjust temporal smoothness in a spatially varying, encoding-dependent manner, reducing the g-factor noise amplification per temporal degree of freedom. This results in a net improvement in tSNR and GLM efficiency, where the efficiency gain can be derived analytically as a function of the encoding and reconstruction parameters. Residual slice leakage and aliasing is limited when fMRI signal energy is dominated by low frequencies. Analytical predictions, simulated and experimental results demonstrate a marked improvement in statistical efficiency in the temporally regularized reconstructions compared to conventional slice-GRAPPA reconstructions, particularly in central brain regions. Furthermore, experimental results confirm that residual slice leakage and aliasing errors are not noticeably increased compared to slice-GRAPPA reconstruction. This approach to temporally regularized image reconstruction in SMS-fMRI improves statistical power, and allows for explicit choice of reconstruction parameters by directly assessing their impact on noise variance per degree of freedom.

Recovering task fMRI signals from highly under-sampled data with low-rank and temporal subspace constraints

Recent developments in highly accelerated fMRI data acquisition have employed low-rank and/or sparsity constraints for image reconstruction, as an alternative to conventional, time-independent parallel imaging. When under-sampling factors are high or the signals of interest are low-variance, however, functional data recovery can be poor or incomplete. We introduce a method for improving reconstruction fidelity using external constraints, like an experimental design matrix, to partially orient the estimated fMRI temporal subspace. Combining these external constraints with low-rank constraints introduces a new image reconstruction model that is analogous to using a mixture of subspace-decomposition (PCA/ICA) and regression (GLM) models in fMRI analysis. We show that this approach improves fMRI reconstruction quality in simulations and experimental data, focusing on the model problem of detecting subtle 1-s latency shifts between brain regions in a block-design task-fMRI experiment. Successful latency discrimination is shown at acceleration factors up to R = 16 in a radial-Cartesian acquisition. We show that this approach works with approximate, or not perfectly informative constraints, where the derived benefit is commensurate with the information content contained in the constraints. The proposed method extends low-rank approximation methods for under-sampled fMRI data acquisition by leveraging knowledge of expected task-based variance in the data, enabling improvements in the speed and efficiency of fMRI data acquisition without the loss of subtle features.

PEAR: PEriodic And fixed Rank separation for fast fMRI

PURPOSE

In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High-quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements.

METHODS

The proposed approach decomposes the fMRI signal into a component which has a fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI.

RESULTS

Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R = 8,10.66 (for simulated data) and R = 6.66,10 (for real data).

CONCLUSIONS

This paper presents PEAR, an undersampled fMRI reconstruction approach based on decomposing the fMRI signal to periodic and fixed rank components. PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank + Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods.

Double temporal sparsity based accelerated reconstruction of compressively sensed resting-state fMRI

A number of reconstruction methods have been proposed recently for accelerated functional Magnetic Resonance Imaging (fMRI) data collection. However, existing methods suffer with the challenge of greater artifacts at high acceleration factors. This paper addresses the issue of accelerating fMRI collection via undersampled k-space measurements combined with the proposed method based on l¹-l¹ norm constraints, wherein we impose first l¹-norm sparsity on the voxel time series (temporal data) in the transformed domain and the second l¹-norm sparsity on the successive difference of the same temporal data. Hence, we name the proposed method as Double Temporal Sparsity based Reconstruction (DTSR) method. The robustness of the proposed DTSR method has been thoroughly evaluated both at the subject level and at the group level on real fMRI data. Results are presented at various acceleration factors. Quantitative analysis in terms of Peak Signal-to-Noise Ratio (PSNR) and other metrics, and qualitative analysis in terms of reproducibility of brain Resting State Networks (RSNs) demonstrate that the proposed method is accurate and robust. In addition, the proposed DTSR method preserves brain networks that are important for studying fMRI data. Compared to the existing methods, the DTSR method shows promising potential with an improvement of 10-12 dB in PSNR with acceleration factors upto 3.5 on resting state fMRI data. Simulation results on real data demonstrate that DTSR method can be used to acquire accelerated fMRI with accurate detection of RSNs.