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

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

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 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

A fast augmented Lagrangian approach for compressed SAR imaging

In this paper we present an accelerated Augmented Lagrangian Method for the solution of constrained convex optimization problems in the Basis Pursuit De-Noising (BPDN) form. The technique relies on on Augmented Lagrangian Methods (ALMs), particularly the Alternating Direction Method of Multipliers (ADMM). Here, we present an application of the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) to SAR imaging, while introducing a method to handle complex SAR imagery in the constrained Total Variation Minimization formulation. In addition, we apply acceleration schemes to C-SALSA to obtain faster convergence of the method; such as used in Fast ADMM methods proposed by Goldstein et al., in the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) proposed by Beck and Teboulle, and in NESTA proposed by Becker et al. We present examples to illustrate the effectiveness of Accelerated C-SALSA in the context of SAR imaging

An alternating direction method of multipliers for sparse SAR imaging (Seyrek SAR görüntüleme için yön değiştiren çarpanlar yaklaşımı)

In this paper, we present a solution to the constrained 1-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), in particular the Alternating Direction Method of Multipliers. Here, we present an application of C-SALSA (an ALM for constrained optimization problems) to SAR imaging. We then compare the performances of several techniques to understand the effectiveness of ALMs in the context of SAR imaging

Autofocused compressive SAR imaging based on the alternating direction method of multipliers

We present an alternating direction method of multipliers (ADMM) based autofocused Synthetic Aperture Radar (SAR) imaging method in the presence of unknown 1-D phase errors in the phase history domain, with undersampled measurements. We formulate the problem as one of joint image formation and phase error estimation. We assume sparsity of strong scatterers in the image domain, and as such use sparsity priors for reconstruction. The algorithm uses l(p)-norm minimization (p <= 1) [8] with an improvement by integrating the phase error updates within the alternating direction method of multipliers (ADMM) steps to correct the unknown 1-D phase error. We present experimental results comparing our proposed algorithm with a coordinate descent based algorithm in terms of convergence speed and reconstruction quality

Curative Chemoradiotherapy of Primary Pancreatic Lymphoma with Vertebral Metastasis: Palliation of Persistent Biliary Stricture by Roux-en-Y Hepaticojejunostomy

Primary pancreatic lymphoma (PPL) is a rare tumor that usually presents with the clinical picture of advanced adenocarcinoma but has a much better prognosis. A 38-year-old man was referred after percutaneous transhepatic external biliary drainage for obstructive jaundice. Abdominal magnetic resonance imaging (MRI) and magnetic resonance cholangiopancreatography had revealed a 5-cm pancreatic head mass that caused biliary tract dilation. Computed tomography angiography showed that the mass encased the celiac trunk as well as the common hepatic and splenic arteries. MRI also revealed a metastatic lesion at the third lumbar vertebra. Serum carcinoembryonic antigen and carbohydrate antigen 19-9 levels were within normal range. The initial diagnosis was inoperable pancreatic adenocarcinoma; however, Tru-Cut pancreatic biopsy showed a large B cell lymphoma. After 6 sessions of chemotherapy and 21 sessions of radiotherapy, both the pancreatic mass and the vertebral metastasis had disappeared. However, he had persistent distal common bile duct stricture that could not be negotiated by either the endoscopic or percutaneous route. A Roux-en-Y hepaticojejunostomy was performed. The patient stayed alive without recurrence for 52 months after the initial diagnosis and 45 months after completion of oncologic treatment. In conclusion, a large pancreatic mass with grossly involved peripancreatic lymph nodes, without ascites, liver or splenic metastasis, should alert the clinician to the possibility of PPL. Cure is possible by chemoradiotherapy even in the presence of vertebral metastasis. Persistent stricture in the distal common bile duct may require a biliodigestive anastomosis

An augmented Lagrangian method for complex-valued compressed SAR imaging

In this paper, we present a solution to the complex synthetic aperture radar (SAR) imaging problem within a constrained optimization formulation where the objective function includes a combination of the ℓ1-norm and the total variation of the magnitude of the complex valued reflectivity field. The technique we present relies on recent advances in the solution of optimization problems, based on Augmented Lagrangian Methods, and in particular on the Alternating Direction Method of Multipliers (ADMM). We rigorously derive the proximal mapping operators, associated with a linear transform of the magnitude of the reflectivity vector and magnitude-total-variation cost functions, for complex-valued SAR images, and thus enable the use of ADMM techniques to obtain computationally efficient solutions for radar imaging. We study the proposed techniques with multiple features (sparse and piecewise-constant in magnitude) based on a weighted sum of the 1-norm and magnitude-total-variation. We derive a fast implementation of the algorithm using only two transforms per iteration for problems admitting unitary transforms as forward models. Experimental results on real data from TerraSAR-X and SARPER-airborne SAR system developed by ASELSAN-demonstrate the effectiveness of the proposed approach