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

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

Pulse shape design using iterative projections

In this paper, the pulse shape design for various communication systems including PAM, FSK, and PSK is considered. The pulse is designed by imposing constraints on the time and frequency domains constraints on the autocorrelation function of the pulse shape. Intersymbol interference, finite duration and spectral mask restrictions are a few examples leading to convex sets in L 2. The autocorrelation function of the pulse is obtained by performing iterative projections onto convex sets. After this step, the minimum phase or maximum phase pulse producing the autocorrelation function is obtained by cepstral deconvolution

Joint reconstruction of multi-contrast images: compressive sensing reconstruction using both joint and individual regularization functions

In many clinical settings, multi-contrast images of a patient are acquired to maximize complementary information. With the underlying anatomy being the same, the mutual information in multi-contrast data can be exploited to improve image reconstruction, especially in accelerated acquisition schemes such as Compressive Sensing (CS). This study proposes a CS-reconstruction algorithm that uses four regularization functions; joint L1-sparsity and TV-regularization terms to exploit the mutual information, and individual L1-sparsity and TV-regularization terms to recover unique features in each image. The proposed method is shown to be robust against leakage-of-features across contrasts, and is demonstrated using simulations and in-vivo experiments