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Two new optimization techniques based on projections onto convex space (POCS)framework for solving convex optimization problems are presented. The dimensionof the minimization problem is lifted by one and sets corresponding to the costfunction are defined. If the cost function is a convex function in R^N thecorresponding set is also a convex set in R^{N+1}. The iterative optimizationapproach starts with an arbitrary initial estimate in R^{N+1} and an orthogonalprojection is performed onto one of the sets in a sequential manner at eachstep of the optimization problem. The method provides globally optimalsolutions in total-variation (TV), filtered variation (FV), L_1, and entropiccost functions. A new denoising algorithm using the TV framework is developed.The new algorithm does not require any of the regularization parameteradjustment. Simulation examples are presented.

Denoising Using Projection Onto Convex Sets (POCS) Based Framework