Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions

Purpose: A time-efficient strategy to acquire high-quality multi-contrast images is to reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause leakage of uncommon features among contrasts, compromising diagnostic utility. The goal of this study is to develop a compressive sensing method for multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Theory: Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi-channel multi-contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. Methods: The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single-channel simulated and multi-channel in-vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. Results: The proposed method demonstrates rapid convergence and improved image quality for both simulated and in-vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage-of-features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms. Conclusion: The proposed compressive sensing method performs fast reconstruction of multi-channel multi-contrast MRI data with improved image quality. It offers reliability against feature leakage in joint reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio

An augmented lagrangian method for sparse SAR imaging

In this paper, we present a solution to the constrained l1-norm minimization problem for sparse SAR imaging. The technique we present relies on recent advances in the solution of optimization problems, based on Augmented Lagrangian Methods (ALMs), namely the Alternating Direction Method of Multipliers. Here, we present an application of C-SALSA (an ALM for constrained optimization problems) to SAR imaging, and introduce a new weighting scheme to improve the sparsity of the reconstructions. We then compare the performances of several techniques to understand the effectiveness of ALMs in the context of SAR imaging

Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections

Cataloged from PDF version of article.Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.Güven, H EmreM.S

Modeling and Propagation of Noisy Waveforms in Static Timing Analysis

A technique based on the sensitivity of the output to input waveform is presented for accurate propagation of delay information through a gate for the purpose of static timing analysis (STA) in the presence of noise. Conventional STA tools represent a waveform by its arrival time and slope. However, this is not an accurate way of modeling the waveform for the purpose of noise analysis. The key contribution of our work is the development of a method that allows efficient propagation of equivalent waveforms throughout the circuit. Experimental results demonstrate higher accuracy of the proposed sensitivity-based gate delay propagation technique, SGDP, compared to the best of existing approaches. SGDP is compatible with the current level of gate characterization in conventional ASIC cell libraries, and as a result, it can be easily incorporated into commercial STA tools to improve their accuracy.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

An augmented Lagrangian method for autofocused compressed SAR imaging

We present an autofocus algorithm for Compressed SAR Imaging. The technique estimates and corrects for 1-D phase errors in the phase history domain, based on prior knowledge that the reflectivity field is sparse, as in the case of strong scatterers against a weakly-scattering background. The algorithm relies on the Sparsity Driven Autofocus (SDA) method and Augmented Lagrangian Methods (ALM), particularly Alternating Directions Method of Multipliers (ADMM). In particular, we propose an ADMM-based algorithm that we call Autofocusing Iteratively Re-Weighted Augmented Lagrangian Method (AIRWALM) to solve a constrained formulation of the sparsity driven autofocus problem with an ℓp-norm, p ≤ 1 cost function. We then compare the performance of the proposed algorithm's performance to Phase Gradient Autofocus (PGA) and SDA [2] in terms of autofocusing capability, phase error correction, and computation time

Yarı Kristal Polimer Malzemelerin Çok Ölçekli Modellenmesi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Bu çalışmada iki fazlı yarı kristal polimerik malzemeler için geometrik olarak doğrusal olmayan, mikromekaniksel motivasyonlu ve çok ölçekli bir malzeme modeli geliştirilmiştir. Bu amaç doğrultusunda, amorf ve kristal fazlar için en önemli şekil değiştirme mekanizmaları belirlenmiş ve bu bilgi ışığında her iki faz için ayrı ayrı mikromekaniksel motivasyonu bulunan malzeme modelleri kullanılmıştır. Ardından, iki fazlı yapıyı homojenleştirerek yarı kristal polimer malzemenin makroskopik davranışını betimleyecek bir model geliştirilmiştir.In this paper a geometrically non-linear micromechanically-motivated multi-scale model is developed for two phase semi-crystalline polymeric materials. To this end, most important deformation mechanisms of amorphous and crystalline phases are determined; and in the light of this information, micromechanically-motivated material models are employed separately for both phases. Afterwards, by homogenization of the two-phase structure, , a model that would render the macroscopic response of the semi crystalline polymeric material is developed

Synthesis of Graphene on Gold

Here we report chemical vapor deposition of graphene on gold surface at ambient pressure. We studied effects of the growth temperature, pressure and cooling process on the grown graphene layers. The Raman spectroscopy of the samples reveals the essential properties of the graphene grown on gold surface. In order to characterize the electrical properties of the grown graphene layers, we have transferred them on insulating substrates and fabricated field effect transistors. Owing to distinctive properties of gold, the ability to grow graphene layers on gold surface could open new applications of graphene in electrochemistry and spectroscopy.Comment: 8 pages, 4 figure

Exponential Separations Using Guarded Extension Variables

We study the complexity of proof systems augmenting resolution with inference rules that allow, given a formula ? in conjunctive normal form, deriving clauses that are not necessarily logically implied by ? but whose addition to ? preserves satisfiability. When the derived clauses are allowed to introduce variables not occurring in ?, the systems we consider become equivalent to extended resolution. We are concerned with the versions of these systems without new variables. They are called BC?, RAT?, SBC?, and GER?, denoting respectively blocked clauses, resolution asymmetric tautologies, set-blocked clauses, and generalized extended resolution. Each of these systems formalizes some restricted version of the ability to make assumptions that hold "without loss of generality," which is commonly used informally to simplify or shorten proofs. Except for SBC?, these systems are known to be exponentially weaker than extended resolution. They are, however, all equivalent to it under a relaxed notion of simulation that allows the translation of the formula along with the proof when moving between proof systems. By taking advantage of this fact, we construct formulas that separate RAT? from GER? and vice versa. With the same strategy, we also separate SBC? from RAT?. Additionally, we give polynomial-size SBC? proofs of the pigeonhole principle, which separates SBC? from GER? by a previously known lower bound. These results also separate the three systems from BC? since they all simulate it. We thus give an almost complete picture of their relative strengths