Compressed sensing (CS) exploits the compressibility of natural signals to reduce the number of samples required for accurate reconstruction. The cost for sub-Nyquist sampling has been computationally expensive recons...
详细信息
ISBN:
(纸本)9781457705953
Compressed sensing (CS) exploits the compressibility of natural signals to reduce the number of samples required for accurate reconstruction. The cost for sub-Nyquist sampling has been computationally expensive reconstruction algorithms, including large-scale l(1) optimization. Therefore, first-order optimization methods that exploit only the gradient of the reconstruction cost function have been developed;notable examples include iterativesoftthresholding (IST), fast iterative soft thresholding algorithm (FISTA), and approximate message passing (AMP). The performance of these algorithms has been studied mainly in the standard framework of convex optimization, called the deterministic framework here. In this paper, we first show that the deterministic approach results in overly pessimistic conclusions that are not indicative of algorithm performance in practice. As an alternative to the deterministic framework, we second study the theoretical aspects of the statistical convergence rate, a topic that has remained unexplored in the sparse recovery literature. Our theoretical and empirical studies reveal several hallmark properties of the statistical convergence of first-order methods, including universality over the matrix ensemble and the least favorable coefficient distribution.
This concise, self-contained volume introduces convex analysis and optimization algorithms, with an emphasis on bridging the two areas. It explores cutting-edge algorithms-such as the proximal gradient, Douglas-Rachfo...
详细信息
ISBN:
(数字)9781611977806
ISBN:
(纸本)9781611977790
This concise, self-contained volume introduces convex analysis and optimization algorithms, with an emphasis on bridging the two areas. It explores cutting-edge algorithms-such as the proximal gradient, Douglas-Rachford, Peaceman-Rachford, and FISTA-that have applications in machine learning, signal processing, image reconstruction, and other fields.
An Introduction to Convexity, Optimization, and algorithms contains
algorithms illustrated by Julia examples,
more than 200 exercises that enhance the reader's understanding of the topic, and
clear explanations and step-by-step algorithmic descriptions that facilitate self-study for individuals looking to enhance their expertise in convex analysis and optimization.
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