On data-selective learning

Adaptive filters are applied in several electronic and communication devices like smartphones, advanced headphones, DSP chips, smart antenna, and teleconference systems. Also, they have application in many areas such as system identification, channel equalization, noise reduction, echo cancellation, interference cancellation, signal prediction, and stock market. Therefore, reducing the energy consumption of the adaptive filtering algorithms has great importance, particularly in green technologies and in devices using battery. In this thesis, data-selective adaptive filters, in particular the set-membership (SM) adaptive filters, are the tools to reach the goal. There are well known SM adaptive filters in literature. This work introduces new algorithms based on the classical ones in order to improve their performances and reduce the number of required arithmetic operations at the same time. Therefore, firstly, we analyze the robustness of the classical SM adaptive filtering algorithms. Secondly, we extend the SM technique to trinion and quaternion systems. Thirdly, by combining SM filtering and partialupdating, we introduce a new improved set-membership affine projection algorithm with constrained step size to improve its stability behavior. Fourthly, we propose some new least-mean-square (LMS) based and recursive least-squares based adaptive filtering algorithms with low computational complexity for sparse systems. Finally, we derive some feature LMS algorithms to exploit the hidden sparsity in the parameters.Filtros adaptativos são aplicados em diversos aparelhos eletrônicos e de comunicação, como smartphones, fone de ouvido avançados, DSP chips, antenas inteligentes e sistemas de teleconferência. Eles também têm aplicação em várias áreas como identificação de sistemas, equalização de canal, cancelamento de eco, cancelamento de interferência, previsão de sinal e mercado de ações. Desse modo, reduzir o consumo de energia de algoritmos adaptativos tem importância significativa, especialmente em tecnologias verdes e aparelhos que usam bateria. Nesta tese, filtros adaptativos com seleção de dados, em particular filtros adaptativos da família set-membership (SM), são apresentados para cumprir essa missão. No presente trabalho objetivamos apresentar novos algoritmos, baseados nos clássicos, a fim de aperfeiçoar seus desempenhos e, ao mesmo tempo, reduzir o número de operações aritméticas exigidas. Dessa forma, primeiro analisamos a robustez dos filtros adaptativos SM clássicos. Segundo, estendemos o SM aos números trinions e quaternions. Terceiro, foram utilizadas também duas famílias de algoritmos, SM filtering e partial-updating, de uma maneira elegante, visando reduzir energia ao máximo possível e obter um desempenho competitivo em termos de estabilidade. Quarto, a tese propõe novos filtros adaptativos baseado em algoritmos least-mean-square (LMS) e mínimos quadrados recursivos com complexidade computacional baixa para espaços esparsos. Finalmente, derivamos alguns algoritmos feature LMS para explorar a esparsidade escondida nos parâmetros

Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)

We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software. Our MATLAB code is available online on GITHUB

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Under-Sampled Reconstruction Techniques for Accelerated Magnetic Resonance Imaging

Due to physical and biological constraints and requirements on the minimum resolution and SNR, the acquisition time is relatively long in magnetic resonance imaging (MRI). Consequently, a limited number of pulse sequences can be run in a clinical MRI session because of constraints on the total acquisition time due to patient comfort and cost considerations. Therefore, it is strongly desired to reduce the acquisition time without compromising the reconstruction quality. This thesis concerns under-sampled reconstruction techniques for acceleration of MRI acquisitions, i.e., parallel imaging and compressed sensing. While compressed sensing MRI reconstructions are commonly regularized by penalizing the decimated wavelet transform coefficients, it is shown in this thesis that the visual artifacts, associated with the lack of translation-invariance of the wavelet basis in the decimated form, can be avoided by penalizing the undecimated wavelet transform coefficients, i.e., the stationary wavelet transform (SWT). An iterative SWT thresholding algorithm for combined SWT-regularized compressed sensing and parallel imaging reconstruction is presented. Additionally, it is shown that in MRI applications involving multiple sequential acquisitions, e.g., quantitative T1/T2 mapping, the correlation between the successive acquisitions can be incorporated as an additional constraint for joint under-sampled reconstruction, resulting in improved reconstruction performance. While quantitative measures of quality, e.g., reconstruction error with respect to the fully-sampled reference, are commonly used for performance evaluation and comparison of under-sampled reconstructions, this thesis shows that such quantitative measures do not necessarily correlate with the subjective quality of reconstruction as perceived by radiologists and other expert end users. Therefore, unless accompanied by subjective evaluations, quantitative quality measurements/comparisons will be of limited clinical impact. The results of experiments aimed at subjective evaluation/comparison of different under-sampled reconstructions for specific clinical neuroimaging MRI applications are presented in this thesis. One motivation behind the current work was to reduce the acquisition time for relaxation mapping techniques DESPOT1 and DESPOT2. This work also includes a modification to the Driven Equilibrium Single Pulse Observation of T1 with high-speed incorporation of RF field inhomogeneities (DESPOT1-HIFI), resulting in more accurate estimation of T1 values at high strength (3T and higher) magnetic fields

Model-Based Super-Resolution Reconstruction of T2 Maps

Purpose High-resolution isotropic T-2 mapping of the human brain with multi-echo spin-echo (MESE) acquisitions is challenging. When using a 2D sequence, the resolution is limited by the slice thickness. If used as a 3D acquisition, specific absorption rate limits are easily exceeded due to the high power deposition of nonselective refocusing pulses. A method to reconstruct 1-mm(3) isotropic T-2 maps is proposed based on multiple 2D MESE acquisitions. Data were undersampled (10-fold) to compensate for the prolonged scan time stemming from the super-resolution acquisition. Theory and Methods The proposed method integrates a classical super-resolution with an iterative model-based approach to reconstruct quantitative maps from a set of undersampled low-resolution data. The method was tested on numerical and multipurpose phantoms, and in vivo data. T-2 values were assessed with a region-of-interest analysis using a single-slice spin-echo and a fully sampled MESE acquisition in a phantom, and a MESE acquisition in healthy volunteers. Results Numerical simulations showed that the best trade-off between acceleration and number of low-resolution datasets is 10-fold acceleration with 4 acquisitions (acquisition time = 18 min). The proposed approach showed improved resolution over low-resolution images for both phantom and brain. Region-of-interest analysis of the phantom compartments revealed that at shorter T-2, the proposed method was comparable with the fully sampled MESE. For the volunteer data, the T-2 values found in the brain structures were consistent across subjects (8.5-13.1 ms standard deviation). Conclusion The proposed method addresses the inherent limitations associated with high-resolution T-2 mapping and enables the reconstruction of 1 mm(3) isotropic relaxation maps with a 10 times faster acquisition