Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to t
he cost function are defined. If the cost function is a convex function in R^N the corresponding set is a convex set in R^(N+1). The iterative optimization approach starts with an arbitrary initial estimate in R^(N+1) and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp, p<1 can be handled by using the supporting hyperplane concept.
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, different
iable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregmans row action D-projection method for compressive sensing applications. Simulation examples are presented.
In this paper, an Entropy functional based online Adaptive Decision Fusion (EADF) framework is developed for image analysis and computer vision applications. In this framework, it is assumed that the compound algorithm consists of several sub-algorit
hms each of which yielding its own decision as a real number centered around zero, representing the confidence level of that particular sub-algorithm. Decision values are linearly combined with weights which are updated online according to an active fusion method based on performing entropic projections onto convex sets describing sub-algorithms. It is assumed that there is an oracle, who is usually a human operator, providing feedback to the decision fusion method. A video based wildfire detection system is developed to evaluate the performance of the algorithm in handling the problems where data arrives sequentially. In this case, the oracle is the security guard of the forest lookout tower verifying the decision of the combined algorithm. Simulation results are presented. The EADF framework is also tested with a standard dataset.
