Future Work

This section concludes the work presented in this thesis with some current and future research directions as well as some possible extentions of each method covered in the previous chapters.

based image denoising technique using a simplified version of the color-Beltrami model. Future work will focus on convex relaxations of the true multichannel-Beltrami model.

• Beltrami regularization was applied locally, meaning that each pixel was re-constructed using the information provided around the pixel of interest. An interesting complication arises, when instead of the very local image intensity, a semi-local image patch is embedded in the optimization itself. The denoising result can therefore be improved by restoring an unknown pixel using other similar pixels in the image. This non-local generalization is however not direct since the noise-free original image does not necessarily have the same similar-ity structures within its noisy version. This non-local patch-based Beltrami extension is currently under investigation.

9.2.2 Myocardial T

Mapping Denoising

• The denoising approach successfully corrected the encountered noise in all sub-jects. In this study, the cardiac noise pattern was mainly studied in post-contrast, after injection of gadolinium, where signal-to-noise ratio is often found higher. The performance of the method in native myocardial T1 mapping was not investigated and should be addressed in future work. Moreover, since the signal does not use signal variation a priori, the proposed strategy can poten-tially benefit to any parametric mapping applications such as T₂ or T^?₂ where precision is influenced by noise.

• The reproducibility and spatial variability of post-contrast T₁ mapping was im-proved using the Beltrami denoising. The use of the anisotropic denoising on T₁-weighted images resulted in higher reproducibility and spatial variability of myocardial T₁ mapping. This work raises some interest in the field of diffusion tensor imaging (DTI), which has the potential of defining structural remodeling of diseased myocardium fiber. Indeed, diffusion tensors describe how much pixel intensities locally diffuse along given orthogonal orientations, and for this rea-son, diffusion tensor are highly related to anisotropic behavior. More advanced comparisons with such techniques deserve further investigation.

• In the first study, we show that Beltrami regularization outperforms the classic total variation regularization in terms of speed and image quality. It would be potentially of interest to compare with recent state-of-the-art denoising method used in computer vision, such as BM3D or non-local reconstruction, where an assumption of local sparsity through similar patches is adopted. Such tech-niques would however require high computation time and would not satisfy fast reconstruction, often required by cardiologists.

• In this study, we established the precision and accuracy of the proposed method with respect to spin echo imaging. Additional phantom evaluation can be done by considering, for example, multi-shot acquisitions as gold-standard.

• The post-acquisition denoising method shows to improve precision of saturation-recovery myocardium T₁ mapping sequence. Precision could also be improved using for instance free-breathing acquisition and motion correction. This would allow multi shots acquisitions with an increased matrix size and could enable the acquisition of more samples on the T1 recovery curve and not being limited to eight saturation times.

• Further investigations in cross-center and cross-vendor study with additional comparisons with inversion-recovery type methods (e.g. MOLLI) are warranted and currently investigated.

should improve motion estimation accuracy on regions suffering from large un-dersampling artifacts. More advanced registration methods and non-cartesian sampling deserve further investigation as well.

• Meanwhile, it would be of great interest to adapt the local Beltrami algorithm to a patch-based non-local regularization which should perform better to recover local image information. Each region of the heart is thus reconstructed and weighted using all similar regions in the image. Besides, dynamic weights can be optimized for our Beltrami regularity by solving a specific minimization problem. This non-locally regularized reconstruction method associated with parallel imaging and motion correction will be investigated in future work.

• One interesting application of the proposed motion correction technique is for high-resolution isotropic 3D late gadolinium enhancement imaging of the heart, such as the one proposed recently in [43] for myocardial scar assessment. This will allow the reconstruction of isotropic motion corrected volumes while keeping the advantages of a 2D acquisition, i.e. high tissue and vessel contrast and short acquisition time.

• A limitation to the method is that potential through-plane motion cannot be corrected, although it remains small compared to the slice thickness. To over-come this problem, one could consider weighting the single-shot images accord-ing to their position in the extracted respiratory signal. The preliminary results presented in this study should be confirmed with further patient studies.

9.2.4 Super-Resolution Cardiac Cine MRI

• The proposed joint motion-correction and super-resolution technique provided reconstruction improvements in terms of image sharpness and image quality of the reconstructed cine volumes. The Beltrami constraint provided efficient denoising without altering the effective resolution. Alternative methods for super-resolution cine imaging include dictionary learning approaches which do not explicitly require motion correction.

• Despite its high efficiently, the b-SSFP sequence used in this study is sensitive to B₀ field inhomogeneity that may result in dark banding artifacts. Although the requirement in terms of B₀ field homogeneity is less important for the 2D b-SSFP than it is for its 3D version, it does rely on efficient shimming in the volume of interest. It should also be noted that both the in-flow effect and the location of the dark-band artifacts depend on the slice orientation and may result in outliers in the native images. This might be overcome with robust super-resolution algorithms.

• Another limitation is that the motion correction and the super-resolution steps were applied sequentially. The final reconstruction might still be improved by merging the two steps into a single optimization problem. Such an approach would consist of searching for the isotropic super-resolution image directly from the motion-corrupted k-space data.