scholarly journals Proximal Algorithms for Discrete-Level Phase-Shifting Mask Design with Application to Optogenetics

Photonics ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 477
Author(s):  
Dimitris Ampeliotis ◽  
Aggeliki Anastasiou ◽  
Christina (Tanya) Politi ◽  
Dimitris Alexandropoulos
Keyword(s):  
Cost Function ◽  
Phase Shifting ◽  
Gradient Algorithm ◽  
Discrete Level ◽  
Proximal Algorithms ◽  
Gradient Algorithms ◽  
Mask Design ◽  
Proximal Gradient Algorithm ◽  
Discrete Phase ◽  
Computer Generated Holograms

This work studies the problem of designing computer-generated holograms using phase-shifting masks limited to represent only a small number of discrete phase levels. This problem has various applications, notably in the emerging field of optogenetics and lithography. A novel regularized cost function is proposed for the problem at hand that penalizes the unfeasible phase levels. Since the proposed cost function is non-smooth, we derive proper proximal gradient algorithms for its minimization. Simulation results, considering an optogenetics application, demonstrate that the proposed proximal gradient algorithm yields better performance as compared to other algorithms proposed in the literature.

Phase-shifting mask design tool

1992 ◽  
Author(s):  
David M. Newmark ◽  
Andrew R. Neureuther
Keyword(s):  
Design Tool ◽  
Phase Shifting ◽  
Mask Design

Numerical experiments on stochastic block proximal-gradient type method for convex constrained optimization involving coordinatewise separable problems

2019 ◽  
Vol 35 (3) ◽  
pp. 371-378
Author(s):  
PORNTIP PROMSINCHAI ◽  
NARIN PETROT ◽  
◽  
◽  
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Objective Functions ◽  
Constrained Optimization Problems ◽  
Type Method ◽  
Coordinate Descent Algorithm ◽  
Proximal Gradient Algorithm ◽  
Separable Problems ◽  
Gradient Type

In this paper, we consider convex constrained optimization problems with composite objective functions over the set of a minimizer of another function. The main aim is to test numerically a new algorithm, namely a stochastic block coordinate proximal-gradient algorithm with penalization, by comparing both the number of iterations and CPU times between this introduced algorithm and the other well-known types of block coordinate descent algorithm for finding solutions of the randomly generated optimization problems with regularization term.

scholarly journals Blind Separation of Positive Sources by Globally Convergent Gradient Search

2004 ◽  
Vol 16 (9) ◽  
pp. 1811-1825 ◽  
Author(s):  
Erkki Oja ◽  
Mark Plumbley
Keyword(s):  
Independent Component Analysis ◽  
Cost Function ◽  
Gradient Flow ◽  
Component Analysis ◽  
Independent Component ◽  
Gradient Algorithm ◽  
Stiefel Manifold ◽  
Blind Separation ◽  
Solution Methods ◽  
Simplified Solution

The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this letter, we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded, which means that they have a nonzero pdf in the region of zero. It can be shown that in this case, the solution method is basically very simple: an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources. We propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint, under which the separating matrix is orthogonal. We further prove that in the Stiefel manifold of orthogonal matrices, the cost function is a Lyapunov function for the matrix gradient flow, implying global convergence. Thus, this algorithm is guaranteed to find the nonnegative well-grounded independent sources. The analysis is complemented by a numerical simulation, which illustrates the algorithm.

scholarly journals Half-quadratic cost function for computing arbitrary phase shifts and phase: Adaptive out of step phase shifting

2006 ◽  
Vol 14 (8) ◽  
pp. 3204 ◽  
Author(s):  
Mariano Rivera ◽  
Rocky Bizuet ◽  
Amalia Martinez ◽  
Juan A. Rayas
Keyword(s):  
Cost Function ◽  
Phase Shifts ◽  
Phase Shifting ◽  
Quadratic Cost ◽  
Arbitrary Phase ◽  
Quadratic Cost Function

scholarly journals Properties and Iterative Methods for theQ-Lasso

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Mohammad Ali Alghamdi ◽  
Naseer Shahzad ◽  
Hong-Kun Xu
Keyword(s):  
Iterative Methods ◽  
Convex Subset ◽  
Gradient Algorithm ◽  
Tuning Parameter ◽  
Linear Measurements ◽  
Tolerance Level ◽  
Basic Properties ◽  
Proximal Gradient Algorithm ◽  
Signal Image

We introduce theQ-lasso which generalizes the well-known lasso of Tibshirani (1996) withQa closed convex subset of a Euclideanm-space for some integerm≥1. This setQcan be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the lasso. Solutions of theQ-lasso depend on a tuning parameterγ. In this paper, we obtain basic properties of the solutions as a function ofγ. Because of ill posedness, we also applyl1-l2regularization to theQ-lasso. In addition, we discuss iterative methods for solving theQ-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm.

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