Real valued diffusion‐weighted imaging using decorrelated phase filtering

Optimal shrinkage denoising breaks the noise floor in high-resolution diffusion MRI

The spatial resolution attainable in diffusion magnetic resonance (MR) imaging is inherently limited by noise. The weaker signal associated with a smaller voxel size, especially at a high level of diffusion sensitization, is often buried under the noise floor owing to the non-Gaussian nature of the MR magnitude signal. Here, we show how the noise floor can be suppressed remarkably via optimal shrinkage of singular values associated with noise in complex-valued k-space data from multiple receiver channels. We explore and compare different low-rank signal matrix recovery strategies to utilize the inherently redundant information from multiple channels. In combination with background phase removal, the optimal strategy reduces the noise floor by 11 times. Our framework enables imaging with substantially improved resolution for precise characterization of tissue microstructure and white matter pathways without relying on expensive hardware upgrades and time-consuming acquisition repetitions, outperforming other related denoising methods.

Does perfect filtering really guarantee perfect phase correction for diffusion MRI data?

Owing to its merit of avoiding noise-floor, phase correction is recently used to reconstruct real-valued diffusion MRI data by employing an image filter to estimate the noise-free background phase. However, several studies report an unexpected signal-loss issue for their reconstruction results, with its causing reason still remaining unclear. Although phase correction has achieved promising results in mitigating the signal-loss issue via improving the employed image filter, we have observed counterintuitive results that an advanced filter generates severe artifacts in our previous work. Considering the potential issues with phase correction procedures, in this paper, we argue that even a perfect image filter is insufficient to produce perfect phase correction. To point out the reason why phase correction introduces signal-loss and address this issue, we first propose a complex polar coordinate system (CPCS) to analyze its procedures in detail; second, based on CPCS, we find that phase correction has not sufficiently utilized the background phase, and thus propose a quantitative criterion to fully exploit the background phase; eventually, we propose a phase calibration procedure to remedy current phase correction. Extensive experimental results, including those on synthetic and real diffusion MRI data, demonstrate that our proposed method significantly reduces signal-loss and also eliminates artifacts in FA maps, particularly with improved accuracy on FA.

SENSE EPI reconstruction with 2D phase error correction and channel-wise noise removal

PURPOSE

To develop a robust reconstruction pipeline for EPI data that enables 2D Nyquist phase error correction using sensitivity encoding without incurring major noise artifacts in low SNR data.

METHODS

SENSE with 2D phase error correction (PEC-SENSE) was combined with channel-wise noise removal using Marcenko-Pastur principal component analysis (MPPCA) to simultaneously eliminate Nyquist ghost artifacts in EPI data and mitigate the noise amplification associated with phase correction using parallel imaging. The proposed pipeline (coined SPECTRE) was validated in phantom DW-EPI data using the accuracy and precision of diffusion metrics; ground truth values were obtained from data acquired with a spin echo readout. Results from the SPECTRE pipeline were compared against PEC-SENSE reconstructions with three alternate denoising strategies: (i) no denoising; (ii) denoising of magnitude data after image formation; (iii) denoising of complex data after image formation. SPECTRE was then tested using highb $$ b $$ -value (i.e., low SNR) diffusion data (up tob = 3000 $$ b=3000 $$  s/mm2 $$ {}^2 $$ ) in four healthy subjects.

RESULTS

Noise amplification associated with phase error correction incurred a 23% bias in phantom mean diffusivity (MD) measurements. Phantom MD estimates using the SPECTRE pipeline were within 8% of the ground truth value. In healthy volunteers, the SPECTRE pipeline visibly corrected Nyquist ghost artifacts and reduced associated noise amplification in highb $$ b $$ -value data.

CONCLUSION

The proposed reconstruction pipeline is effective in correcting low SNR data, and improves the accuracy and precision of derived diffusion metrics.

Adaptive phase correction of diffusion-weighted images

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

Computation of exact g-factor maps in 3D GRAPPA reconstructions

PURPOSE

To characterize the noise distributions in 3D-MRI accelerated acquisitions reconstructed with GRAPPA using an exact noise propagation analysis that operates directly in k-space.

THEORY AND METHODS

We exploit the extensive symmetries and separability in the reconstruction steps to account for the correlation between all the acquired k-space samples. Monte Carlo simulations and multi-repetition phantom experiments were conducted to test both the accuracy and feasibility of the proposed method; a high-resolution in-vivo experiment was performed to assess the applicability of our method to clinical scenarios.

RESULTS

Our theoretical derivation shows that the direct k-space analysis renders an exact noise characterization under the assumptions of stationarity and uncorrelation in the original k-space. Simulations and phantom experiments provide empirical support to the theoretical proof. Finally, the high-resolution in-vivo experiment demonstrates the ability of the proposed method to assess the impact of the sub-sampling pattern on the overall noise behavior.

CONCLUSIONS

By operating directly in the k-space, the proposed method is able to provide an exact characterization of noise for any Cartesian pattern sub-sampled along the two phase-encoding directions. Exploitation of the symmetries and separability into independent blocks through the image reconstruction procedure allows us to overcome the computational challenges related to the very large size of the covariance matrices involved.

Exact Calculation of Noise Maps and ${g}$ -Factor in GRAPPA Using a ${k}$ -Space Analysis

Characterization of the noise distribution in magnetic resonance images has multiple applications, including quality assurance and protocol optimization. Noise characterization is particularly important in the presence of parallel imaging acceleration with multi-coil acquisitions, where the noise distribution can contain severe spatial heterogeneities. If the parallel imaging reconstruction is a linear process, an accurate noise analysis can be carried out by taking into account the correlations between all the samples involved. However, for -space-based techniques such as generalized autocalibrating partially parallel acquisition (GRAPPA), the exact analysis has been considered computationally prohibitive due to the very large size of the noise covariance matrices required to characterize the noise propagation from -space to image space. Previously proposed methods avoid this computational burden by formulating the GRAPPA reconstruction as a pixel-wise linear operation performed in the image space. However, these methods are not exact in the presence of non-uniform sampling of -space (e.g., containing a calibration region). For this reason, in this paper, we develop an accurate characterization of the noise distribution for self-calibrated parallel imaging in the presence of arbitrary Cartesian sampling patterns. By exploiting the symmetries and separability in the noise propagation process, the proposed method is computationally efficient and does not require large matrices. Under the assumption of a fixed reconstruction kernel, this method provides the precise distribution of the noise variance for each coil's image. These coil-by-coil noise maps are subsequently combined according to the coil combination approach used in image reconstruction, and therefore can be applied with both complex coil combination and root-sum-of-squares approaches. In this paper, we present the proposed noise characterization method and compare it to previous techniques using Monte Carlo simulations as well as phantom acquisitions.

A 1-minute full brain MR exam using a multicontrast EPI sequence

PURPOSE

A new multicontrast echo-planar imaging (EPI)-based sequence is proposed for brain MRI, which can directly generate six MR contrasts (T₁ -FLAIR, T₂ -w, diffusion-weighted (DWI), apparent diffusion coefficient (ADC), T2*-w, T₂ -FLAIR) in 1 min with full brain coverage. This could enable clinical MR clinical screening in similar time as a conventional CT exam but with more soft-tissue information.

METHODS

Eleven sequence modules were created as dynamic building blocks for the sequence. Two EPI readout modules were reused throughout the sequence and were prepended by other modules to form the desired MR contrasts. Two scan protocols were optimized with scan times of 55-75 s. Motion experiments were carried out on two volunteers to investigate the robustness against head motion. Scans on patients were carried out and compared to conventional clinical images.

RESULTS

The pulse sequence is found to be robust against motion given its single-shot nature of each contrast. For excessive out-of-plane head motion, the T₁ -FLAIR and T₂ -FLAIR contrasts suffer from incomplete inversion. Despite lower signal-to-noise ratio (SNR) and resolution, the 1-min multicontrast EPI data show promising correspondence with conventional diagnostic scans on patients.

CONCLUSION

A 1 min multicontrast brain MRI scan based on EPI readouts has been presented in this feasibility study. Preliminary data show potential for clinical brain MRI use with minimal bore time for the patient. Such short examination time could be useful (e.g., for screening and acute stroke). The sequence may also help planning conventional brain MRI scans if run at the beginning of an examination. Magn Reson Med 79:3045-3054, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Model-based denoising in diffusion-weighted imaging using generalized spherical deconvolution

PURPOSE

Diffusion MRI often suffers from low signal-to-noise ratio, especially for high b-values. This work proposes a model-based denoising technique to address this limitation.

METHODS

A generalization of the multi-shell spherical deconvolution model using a Richardson-Lucy algorithm is applied to noisy data. The reconstructed coefficients are then used in the forward model to compute denoised diffusion-weighted images (DWIs). The proposed method operates in the diffusion space and thus is complementary to image-based denoising methods.

RESULTS

We demonstrate improved image quality on the DWIs themselves, maps of neurite orientation dispersion and density imaging, and diffusional kurtosis imaging (DKI), as well as reduced spurious peaks in deterministic tractography. For DKI in particular, we observe up to 50% error reduction and demonstrate high image quality using just 30 DWIs. This corresponds to greater than fourfold reduction in scan time if compared to the widely used 140-DWI acquisitions. We also confirm consistent performance in pathological data sets, namely in white matter lesions of a multiple sclerosis patient.

CONCLUSION

The proposed denoising technique termed generalized spherical deconvolution has the potential of significantly improving image quality in diffusion MRI. Magn Reson Med 78:2428-2438, 2017. © 2017 International Society for Magnetic Resonance in Medicine.