Convex Feasibility Methods for Compressed Sensing
نویسندگان
چکیده
Manuscript received ; revised . Copyright (c) 2010 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. A. Carmi is with the Asher Space Research Institute, Technion – Israel Institute of Technology, Haifa 32000, Israel. P. Gurfil is with the Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel.
منابع مشابه
Convex feasibility modeling and projection methods for sparse signal recovery
A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimizati...
متن کاملA Block-Wise random sampling approach: Compressed sensing problem
The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...
متن کاملAccelerating Magnetic Resonance Imaging through Compressed Sensing Theory in the Direction space-k
Magnetic Resonance Imaging (MRI) is a noninvasive imaging method widely used in medical diagnosis. Data in MRI are obtained line-by-line within the K-space, where there are usually a great number of such lines. For this reason, magnetic resonance imaging is slow. MRI can be accelerated through several methods such as parallel imaging and compressed sensing, where a fraction of the K-space lines...
متن کاملA Geometrical Stability Condition for Compressed Sensing
During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors x ∈ R, the concept has been extended to cover many other types of problems. A noteable example is low-rank matrix recovery. Many methods used for recovery rel...
متن کاملRenegar’s Condition Number, Sharpness and Compressed Sensing Performance
We show that several quantities controlling compressed sensing performance also directly control algorithmic complexity. We describe linearly convergent restart schemes solving a broad range of compressed sensing problems using first-order methods. The key term controlling convergence measures the sharpness of the optimum and can be interpreted as a condition number, computed as the ratio betwe...
متن کامل