Frequency-splitting Dynamic MRI Reconstruction using Multi-scale 3D Convolutional Sparse Coding and Automatic Parameter Selection

Department of Computer Science and EngineeringIn this thesis, we propose a novel image reconstruction algorithm using multi-scale 3D con- volutional sparse coding and a spectral decomposition technique for highly undersampled dy- namic Magnetic Resonance Imaging (MRI) data. The proposed method recovers high-frequency information using a shared 3D convolution-based dictionary built progressively during the re- construction process in an unsupervised manner, while low-frequency information is recovered using a total variation-based energy minimization method that leverages temporal coherence in dynamic MRI. Additionally, the proposed 3D dictionary is built across three different scales to more efficiently adapt to various feature sizes, and elastic net regularization is employed to promote a better approximation to the sparse input data. Furthermore, the computational com- plexity of each component in our iterative method is analyzed. We also propose an automatic parameter selection technique based on a genetic algorithm to find optimal parameters for our numerical solver which is a variant of the alternating direction method of multipliers (ADMM). We demonstrate the performance of our method by comparing it with state-of-the-art methods on 15 single-coil cardiac, 7 single-coil DCE, and a multi-coil brain MRI datasets at different sampling rates (12.5%, 25% and 50%). The results show that our method significantly outper- forms the other state-of-the-art methods in reconstruction quality with a comparable running time and is resilient to noise.ope

Robust sparse image reconstruction of radio interferometric observations with purify

Next-generation radio interferometers, such as the Square Kilometre Array (SKA), will revolutionise our understanding of the universe through their unprecedented sensitivity and resolution. However, to realise these goals significant challenges in image and data processing need to be overcome. The standard methods in radio interferometry for reconstructing images, such as CLEAN, have served the community well over the last few decades and have survived largely because they are pragmatic. However, they produce reconstructed inter\-ferometric images that are limited in quality and scalability for big data. In this work we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software package. In particular, we implement and apply the proximal alternating direction method of multipliers (P-ADMM) algorithm presented in a recent article. First, we assess the impact of the interpolation kernel used to perform gridding and degridding on sparse image reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as well as prolate spheroidal wave functions, while providing a computational saving and an analytic form. Second, we apply PURIFY to real interferometric observations from the Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA) and find images recovered by PURIFY are higher quality than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions exhibit additional advantages over those recovered by CLEAN. The latest version of PURIFY, with developments presented in this work, is made publicly available.Comment: 22 pages, 10 figures, PURIFY code available at http://basp-group.github.io/purif

SOWAT: Speckle Observations With Alleviated Turbulence

Adaptive optics (AO) systems and image reconstruction algorithms are indispensable tools when it comes to high-precision astrometry. In this paper, we analyze the potential of combining both techniques, i.e. by applying image reconstruction on partially AO corrected short exposures. Therefore we simulate speckle clouds with and without AO corrections and create synthetic observations. We apply holographic image reconstruction to the obtained observations and find that (i) the residual wavefronts decorrelate slowlier and to a lower limit when AO systems are used, (ii) the same reference stars yield a better reconstruction, and (iii) using fainter reference stars we achieve a similar image quality. These results suggest that holographic imaging of speckle observations is feasible with 2-3 times longer integration times and 3mag fainter reference stars, to obtain diffraction-limited imaging from low-order AO systems that are less restricted in sky-coverage than typical high-order AO systems.Comment: 18 pages, 13 figures, and 3 table

Acoustical structured illumination for super-resolution ultrasound imaging.

Structured illumination microscopy is an optical method to increase the spatial resolution of wide-field fluorescence imaging beyond the diffraction limit by applying a spatially structured illumination light. Here, we extend this concept to facilitate super-resolution ultrasound imaging by manipulating the transmitted sound field to encode the high spatial frequencies into the observed image through aliasing. Post processing is applied to precisely shift the spectral components to their proper positions in k-space and effectively double the spatial resolution of the reconstructed image compared to one-way focusing. The method has broad application, including the detection of small lesions for early cancer diagnosis, improving the detection of the borders of organs and tumors, and enhancing visualization of vascular features. The method can be implemented with conventional ultrasound systems, without the need for additional components. The resulting image enhancement is demonstrated with both test objects and ex vivo rat metacarpals and phalanges