Sparse and low-rank techniques for the efficient restoration of images

Image reconstruction is a key problem in numerous applications of computer vision and medical imaging. By removing noise and artifacts from corrupted images, or by enhancing the quality of low-resolution images, reconstruction methods are essential to provide high-quality images for these applications. Over the years, extensive research efforts have been invested toward the development of accurate and efficient approaches for this problem. Recently, considerable improvements have been achieved by exploiting the principles of sparse representation and nonlocal self-similarity. However, techniques based on these principles often suffer from important limitations that impede their use in high-quality and large-scale applications. Thus, sparse representation approaches consider local patches during reconstruction, but ignore the global structure of the image. Likewise, because they average over groups of similar patches, nonlocal self-similarity methods tend to over-smooth images. Such methods can also be computationally expensive, requiring a hour or more to reconstruct a single image. Furthermore, existing reconstruction approaches consider either local patch-based regularization or global structure regularization, due to the complexity of combining both regularization strategies in a single model. Yet, such combined model could improve upon existing techniques by removing noise or reconstruction artifacts, while preserving both local details and global structure in the image. Similarly, current approaches rarely consider external information during the reconstruction process. When the structure to reconstruct is known, external information like statistical atlases or geometrical priors could also improve performance by guiding the reconstruction. This thesis addresses limitations of the prior art through three distinct contributions. The first contribution investigates the histogram of image gradients as a powerful prior for image reconstruction. Due to the trade-off between noise removal and smoothing, image reconstruction techniques based on global or local regularization often over-smooth the image, leading to the loss of edges and textures. To alleviate this problem, we propose a novel prior for preserving the distribution of image gradients modeled as a histogram. This prior is combined with low-rank patch regularization in a single efficient model, which is then shown to improve reconstruction accuracy for the problems of denoising and deblurring. The second contribution explores the joint modeling of local and global structure regularization for image restoration. Toward this goal, groups of similar patches are reconstructed simultaneously using an adaptive regularization technique based on the weighted nuclear norm. An innovative strategy, which decomposes the image into a smooth component and a sparse residual, is proposed to preserve global image structure. This strategy is shown to better exploit the property of structure sparsity than standard techniques like total variation. The proposed model is evaluated on the problems of completion and super-resolution, outperforming state-of-the-art approaches for these tasks. Lastly, the third contribution of this thesis proposes an atlas-based prior for the efficient reconstruction of MR data. Although popular, image priors based on total variation and nonlocal patch similarity often over-smooth edges and textures in the image due to the uniform regularization of gradients. Unlike natural images, the spatial characteristics of medical images are often restricted by the target anatomical structure and imaging modality. Based on this principle, we propose a novel MRI reconstruction method that leverages external information in the form of an probabilistic atlas. This atlas controls the level of gradient regularization at each image location, via a weighted total-variation prior. The proposed method also exploits the redundancy of nonlocal similar patches through a sparse representation model. Experiments on a large scale dataset of T1-weighted images show this method to be highly competitive with the state-of-the-art

Depth Superresolution using Motion Adaptive Regularization

Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side information. In this paper, we demonstrate that further incorporating temporal information in videos can significantly improve the results. In particular, we propose a novel approach that improves depth resolution, exploiting the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. Experiments confirm that the proposed approach substantially improves the quality of the estimated high-resolution depth. Our approach can be a first component in systems using vision techniques that rely on high resolution depth information

AliasNet: Alias Artefact Suppression Network for Accelerated Phase-Encode MRI

Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that combination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application