Polynomial spline-approximation of Clarke's model

We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling factor increases, the optimal and interpolation splines of even order tend to provide the same accuracy. To build such splines, the process to be approximated needs to be known for all time, which is impractical. Local splines, on the other hand, may be used where the process is known only over a finite interval. We first consider local splines with quasioptimal spline coefficients. Then, we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients. In practice, approximation with a low processing delay is of interest; we investigate local spline extrapolation with a zero-processing delay. The results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error; the error can be very close to the minimum error provided by optimal splines. Thus, local splines can be effectively used for channel estimation in multipath fast fading channels

Multiple Selection Extrapolation for Improved Spatial Error Concealment

This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby, the model results from a weighted superposition of two-dimensional basis functions whereas in every iteration step a set of these is selected and the approximation residual is projected onto the subspace they span. The algorithm is an improvement to the Frequency Selective Extrapolation that has proven to be an effective method for concealing lost or distorted image regions. Compared to this algorithm, the novel algorithm is able to reduce the processing time by a factor larger than three, by still preserving the very high extrapolation quality

An importance sampling algorithm for generating exact eigenstates of the nuclear Hamiltonian

We endow a recently devised algorithm for generating exact eigensolutions of large matrices with an importance sampling, which is in control of the extent and accuracy of the truncation of their dimensions. We made several tests on typical nuclei using a correlated basis obtained from partitioning the shell model space. The sampling so implemented allows not only for a substantial reduction of the shell model space but also for an extrapolation to exact eigenvalues and E2 strengths.Comment: A compressed file composed of a text in latex of 19 pages and 9 figures in p

Advanced parallel magnetic resonance imaging methods with applications to MR spectroscopic imaging

Parallel magnetic resonance imaging offers a framework for acceleration of conventional MRI encoding using an array of receiver coils with spatially-varying sensitivities. Novel encoding and reconstruction techniques for parallel MRI are investigated in this dissertation. The main goal is to improve the actual reconstruction methods and to develop new approaches for massively parallel MRI systems that take advantage of the higher information content provided by the large number of small receivers. A generalized forward model and inverse reconstruction with regularization for parallel MRI with arbitrary k-space sub-sampling is developed. Regularization methods using the singular value decomposition of the encoding matrix and pre-conditioning of the forward model are proposed to desensitize the solution from data noise and model errors. Variable density k-space sub-sampling is presented to improve the reconstruction with the common uniform sub-sampling. A novel method for massively parallel MRI systems named Superresolution Sensitivity Encoding (SURE-SENSE) is proposed where acceleration is performed by acquiring the low spatial resolution representation of the object being imaged and the stronger sensitivity variation from small receiver coils is used to perform intra-pixel reconstruction. SURE-SENSE compares favorably the performance of standard SENSE reconstruction for low spatial resolution imaging such as spectroscopic imaging. The methods developed in this dissertation are applied to Proton Echo Planar Spectroscopic Imaging (PEPSI) for metabolic imaging in human brain with high spatial and spectral resolution in clinically feasible acquisition times. The contributions presented in this dissertation are expected to provide methods that substantially enhance the utility of parallel MRI for clinical research and to offer a framework for fast MRSI of human brain with high spatial and spectral resolution

Fast image reconstruction with L2-regularization

Purpose We introduce L2-regularized reconstruction algorithms with closed-form solutions that achieve dramatic computational speed-up relative to state of the art L1- and L2-based iterative algorithms while maintaining similar image quality for various applications in MRI reconstruction. Materials and Methods We compare fast L2-based methods to state of the art algorithms employing iterative L1- and L2-regularization in numerical phantom and in vivo data in three applications; (i) Fast Quantitative Susceptibility Mapping (QSM), (ii) Lipid artifact suppression in Magnetic Resonance Spectroscopic Imaging (MRSI), and (iii) Diffusion Spectrum Imaging (DSI). In all cases, proposed L2-based methods are compared with the state of the art algorithms, and two to three orders of magnitude speed up is demonstrated with similar reconstruction quality. Results The closed-form solution developed for regularized QSM allows processing of a three-dimensional volume under 5 s, the proposed lipid suppression algorithm takes under 1 s to reconstruct single-slice MRSI data, while the PCA based DSI algorithm estimates diffusion propagators from undersampled q-space for a single slice under 30 s, all running in Matlab using a standard workstation. Conclusion For the applications considered herein, closed-form L2-regularization can be a faster alternative to its iterative counterpart or L1-based iterative algorithms, without compromising image quality.National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant NIBIB K99EB012107)National Institutes of Health (U.S.) (Grant NIH R01 EB007942)National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant NIBIB R01EB006847)Grant K99/R00 EB008129National Center for Research Resources (U.S.) (Grant NCRR P41RR14075)National Institutes of Health (U.S.) (Blueprint for Neuroscience Research U01MH093765)Siemens CorporationSiemens-MIT AllianceMIT-Center for Integration of Medicine and Innovative Technology (Medical Engineering Fellowship

Comparative Study of OpenCV Inpainting Algorithms

Digital image processing has been a significant and important part in the realm of computing science since its inception. It entails the methods and techniques that are used to manipulate a digital image using a digital computer. It is a type of signal processing in which the input and output maybe image or features/characteristics associated with that image. In this age of advanced technology, digital image processing has its uses manifold, some major fields being image restoration, medical field, computer vision, color processing, pattern recognition and video processing. Image inpainting is one such important domain of image processing. It is a form of image restoration and conservation. This paper presents a comparative study of the various digital inpainting algorithms provided by Open CV (a popular image processing library) and also identifies the most effective inpainting algorithm on the basis of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM) and runtime metrics

Lipid suppression in CSI with spatial priors and highly undersampled peripheral k-space

Mapping [superscript 1]H brain metabolites using chemical shift imaging is hampered by the presence of subcutaneous lipid signals, which contaminate the metabolites by ringing due to limited spatial resolution. Even though chemical shift imaging at spatial resolution high enough to mitigate the lipid artifacts is infeasible due to signal-to-noise constraints on the metabolites, the lipid signals have orders of magnitude of higher concentration, which enables the collection of high-resolution lipid maps with adequate signal-to-noise. The previously proposed dual-density approach exploits this high signal-to-noise property of the lipid layer to suppress truncation artifacts using high-resolution lipid maps. Another recent approach for lipid suppression makes use of the fact that metabolite and lipid spectra are approximately orthogonal, and seeks sparse metabolite spectra when projected onto lipid-basis functions. This work combines and extends the dual-density approach and the lipid-basis penalty, while estimating the high-resolution lipid image from 2-average k-space data to incur minimal increase on the scan time. Further, we exploit the spectral-spatial sparsity of the lipid ring and propose to estimate it from substantially undersampled (acceleration R = 10 in the peripheral k-space) 2-average in vivo data using compressed sensing and still obtain improved lipid suppression relative to using dual-density or lipid-basis penalty alone.National Institutes of Health (U.S.) (Grant NIH R01 EB007942)National Science Foundation (U.S.) (Grant 0643836)Siemens-MIT AllianceMIT-Center for Integration of Medicine and Innovative Technology (Medical Engineering Fellowship