Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that  wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term.  apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the   $\boldsymbol{\ell }_1$   -norm penalty on the signal's linear transform coefficients. The PNPG approach employs a projected Nesterov's acceleration step with restart and a duality-based inner iteration to compute the proximal mapping.  propose an  adaptive  step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG converges faster than the methods that do not adjust to the local curvature of the NLL.  present an integrated derivation of the momentum acceleration and proofs of   $\boldsymbol{\mathcal {O}(k^{-2})}$    objective function convergence rate and convergence of the iterates, which account for adaptive step size, inexactness of the iterative proximal mapping, and the convex-set constraint. The tuning of PNPG is largely application independent. Tomographic and compressed-sensing reconstruction experiments with Poisson generalized linear and Gaussian linear measurement models demonstrate the performance of the proposed approach.
['Renliang Gu', 'Aleksandar Dogandzic']
I am writing a research paper on a idea Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery
[{"from": "human", "value": "I am writing a research paper on a idea Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that  wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term.  apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the   $\\boldsymbol{\\ell }_1$   -norm penalty on the signal's linear transform coefficients. The PNPG approach employs a projected Nesterov's acceleration step with restart and a duality-based inner iteration to compute the proximal mapping.  propose an  adaptive  step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG converges faster than the methods that do not adjust to the local curvature of the NLL.  present an integrated derivation of the momentum acceleration and proofs of   $\\boldsymbol{\\mathcal {O}(k^{-2})}$    objective function convergence rate and convergence of the iterates, which account for adaptive step size, inexactness of the iterative proximal mapping, and the convex-set constraint. The tuning of PNPG is largely application independent. Tomographic and compressed-sensing reconstruction experiments with Poisson generalized linear and Gaussian linear measurement models demonstrate the performance of the proposed approach."}]