In the computation, the projection (P_{C}) where C is a closed ball in (mathbb{R}^{N}), and in the projections (P_{C_{n}}) and (P_{Q_{n}}) where (C_{n}) and (Q_{n}) are the halfspaces in (mathbb{R}^{N}) and (mathbb {R}^{M}), respectively, we use the formulation as follows.
Therefore, for each k, (T_{k}) is closed and convex set, and the computation of projection (y^{k}=P_{T_{k}}(x^{k}-alpha_{k}w^{k})) in Step 2 of Algorithm 3.2 is explicit and easier than the computation of projection (y^{k}=P_{C}(x^{k}-alpha_{k}w^{k})) in Step 2 of Algorithm 3.1 when C has a complex structure.
Throughout this computation, the projection maps (P_{omega }) that associates a 3D point (mathbf{X}) to a 2D pixel (mathbf{x}) in micrograph (omega) are taken affine, i.e., rays are considered as straight lines.
Based on these premises, we recognize that the sparse structure of the matrix Φ R results into two main features of Radon-like projection computation in a WSN: The computation of each projection y ( ϑ p ) [ m ] is performed in a distributed way within the WSN, and it requires signaling among grid sensors which are adjacent along a WSN path.
The main contribution of this novel method is the automatic computation of the projection vector.
From here, an H2 optimization problem with defined constraints is formulated, and an efficient iterative solver is proposed by hybridizing direct computation of constrained projection gradient and line search of optimal step.
After forward projection computation, back projection is performed.
However, Algorithm 1.9 is involved with the computation of metric projection.
The computation of a projection onto a general closed convex subset is generally difficult.
Thereby, we resort to a spatially sparse signal CS scheme inspired by the Radon projection computation.
