Alper Gungor

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

An Augmented Lagrangian Method for image reconstruction with multiple features

\ell _1

An efficient parallel algorithm for single-pixel and FPA imaging

-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.

A synthesis-based approach to compressive multi-contrast magnetic resonance imaging

We present an Augmented Lagrangian Method (ALM) for solving image reconstruction problems with a cost function consisting of multiple regularization functions with a data fidelity constraint. The presented technique is used to solve inverse problems related to image reconstruction, including compressed sensing formulations. Our contributions include an improvement for reducing the number of computations required by an existing ALM method, an approach for obtaining the proximal mapping associated with p-norm based regularizers, and lastly a particular ALM for the constrained image reconstruction problem with a hybrid cost function including a weighted sum of the p-norm and the total variation of the image. We present examples from Synthetic Aperture Radar imaging and Computed Tomography.

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

Long image acquisition time is a critical problem in single-pixel-imaging. Here, we propose a new high-speed single-pixel compressive imaging method. We develop an ADMM based optimization algorithm to handle images with multiple features. The proposed method solves an optimization problem with the objectives of Total- Variation and ℓ1-norm with a data-fidelity constraint. The algorithm is highly parallel and is suitable for implementation using GPUs, with a significant reduction in computation. The resulting system produces high resolution images and can also be used for super-resolution by changing the single detector with a focal plane array. We verify the system experimentally and compare the performance of our algorithm with similar methods.

An efficient algorithm for model based blind deconvolution

In this study, we deal with the problem of image reconstruction from compressive measurements of multi-contrast magnetic resonance imaging (MRI). We propose a synthesis based approach for image reconstruction to better exploit mutual information across contrasts, while retaining individual features of each contrast image. For fast recovery, we propose an augmented Lagrangian based algorithm, using Alternating Direction Method of Multipliers (ADMM). We then compare the proposed algorithm to the state-of-the-art Compressive Sensing-MRI algorithms, and show that the proposed method results in better quality images in shorter computation time.

Feature-enhanced computational infrared imaging

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 ℓp-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.

Fast recovery of compressed multi-contrast magnetic resonance images

We propose a method for partially blind-deconvolution with prior information on the lens characteristics. There is a permanent demand for higher resolution for applications such as tracking, recognition, and identification. Limitations of available methods for practical systems are generally due to computational cost and power. Therefore a computationally efficient method for blind-deconvolution is desirable for practical systems. Total-variation (TV) minimization method proposed by Vogel and Oman is used to recover the image from noisy data and eliminated some of the blurs. Another approach called split augmented Lagrangian shrinkage algorithm uses alternating direction method of multipliers (ADMM) in which an unconstrained optimization problem including ℓ1 data fidelity and a non-smooth regularization term are solved. Although successful, the excessive computational requirements present a challenge for practical usage of these methods. Here, we propose a parametric blind-deconvolution method with prior knowledge on the point spread function (PSF) of the camera lens. We model the PSF of the circular optics as Jinc-squared function and determine the best PSF by solving optimization problem containing TV-norm along with Wavelet-sparsity objectives using an ADMM based algorithm. We use a convolutional model and work in Fourier domain for efficient implementation, and avoid circular effects by extending the unknown image region. First, we show that PSF function of the lenses can be modeled with Jinc function in experimental data. Next, we point out that our algorithm improves resolution of the image and compared to classical blind-deconvolution methods while remaining feasible in terms of computation time.

Passive localization and classification of cavitation activity using group sparsity

Super-resolution for infrared imaging is motivated by the high cost and practical limitations of obtai ning large focal plane arrays. Methods in the literature require the optic al system to be modified. Here, we propose a compre ssiv sensing based method for super-resolution using the inherent poin t spread function of the camera. The proposed metho d pr duces high resolution images and is robust against missing pix els. We then compare our method to other super-reso lution methods in the literature and show that our method performs well f or practical usage without any modification to the optical system.Super-resolution for infrared imaging is motivated by the high cost and practical limitations of obtaining large focal plane arrays. Methods in the literature require the optical system to be modified. Here, we propose a compressive sensing based method for super-resolution using the inherent point spread function of the camera. The proposed method produces high resolution images and is robust against missing pixels. We then compare our method to other super-resolution methods in the literature and show that our method performs well for practical usage without any modification to the optical system.

Compressed Multi-Contrast Magnetic Resonance Image reconstruction using Augmented Lagrangian Method

In many settings, multiple Magnetic Resonance Imaging (MRI) scans are performed with different contrast characteristics at a single patient visit. Unfortunately, MRI data-acquisition is inherently slow creating a persistent need to accelerate scans. Multi-contrast reconstruction deals with the joint reconstruction of different contrasts simultaneously. Previous approaches suggest solving a regularized optimization problem using group sparsity and/or color total variation, using composite-splitting denoising and FISTA. Yet, there is significant room for improvement in existing methods regarding computation time, ease of parameter selection, and robustness in reconstructed image quality. Selection of sparsifying transformations is critical in applications of compressed sensing. Here we propose using non-convex p-norm group sparsity (with p < 1), and apply color total variation (CTV). Our method is readily applicable to magnitude images rather than each of the real and imaginary parts separately. We use the constrained form of the problem, which allows an easier choice of data-fidelity error-bound (based on noise power determined from a noise-only scan without any RF excitation). We solve the problem using an adaptation of Alternating Direction Method of Multipliers (ADMM), which provides faster convergence in terms of CPU-time. We demonstrated the effectiveness of the method on two MR image sets (numerical brain phantom images and SRI24 atlas data) in terms of CPU-time and image quality. We show that a non-convex group sparsity function that uses the p-norm instead of the convex counterpart accelerates convergence and improves the peak-Signal-to-Noise-Ratio (pSNR), especially for highly undersampled data.