A fast, low-complexity, algorithm for solving the `1-regularized least-squares problem is devised and analyzed. Our algorithm, which we call the Inertial Iterative Soft-Thresholding Algorithm (I-ISTA), incorporates inertia into a forward-backward proximal splitting framework. We show that I-ISTA has a linear rate of convergence with a smaller asymptotic error constant than the well-known Iterat...

We establish local linear convergence bounds for the ISTA and FISTA iterations on the model LASSO problem. We show that FISTA can be viewed as an accelerated ISTA process. Using a spectral analysis, we show that, when close enough to the solution, both iterations converge linearly, but FISTA slows down compared to ISTA, making it advantageous to switch to ISTA toward the end of the iteration pr...

Traditional methods for image compressive sensing (CS) reconstruction solve a welldefined inverse problem (convex optimization problems in many cases) that is based on a predefined CS model, which defines the underlying structure of the problem and is generally solved by employing convergent iterative solvers. These optimization-based CS methods face the challenge of choosing optimal transforms...

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...

Many unintended and undesired consequences of Healthcare Information Technologies (HIT) flow from interactions between the HIT and the healthcare organization's sociotechnical system-its workflows, culture, social interactions, and technologies. This paper develops and illustrates a conceptual model of these processes that we call Interactive Sociotechnical Analysis (ISTA). ISTA captures common...

The iterative shrinkage/thresholding algorithm (ISTA) and its faster version FISTA have been widely used in the literature. In this paper, we consider general versions of the ISTA and FISTA in the more general “strongly + semi” convex setting, i.e., minimizing the sum of a strongly convex function and a semiconvex function; and conduct convergence analysis for them. The consideration of a semic...

31st ISTA Congress Tallinn, Estonia 15–17 June 2016

We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also kno...