Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  treat the phase retrieval (PR) problem of reconstructing the interest signal from its Fourier magnitude. Since the Fourier phase information is lost, the problem is ill-posed. Several techniques have been used to address this problem by utilizing various priors such as non-negative, support, and Fourier magnitude constraints. Recent methods exploiting sparsity are developed to improve the reconstruction quality. Hover, the previous algorithms of utilizing sparsity prior suffer from either the low reconstruction quality at low oversampled factors or being sensitive to noise. To address these issues,  propose a framework that exploits sparsity of the signal in the translation invariant Haar pyramid (TIHP) tight frame. Based on this sparsity prior,  formulate the sparse representation regularization term and incorporate it into the PR optimization problem.  propose the alternating iterative algorithm for solving the corresponding non-convex problem by dividing the problem into several subproblems.  give the optimal solution to each subproblem, and experimental simulations under the noise-free and noisy scenario indicate that our proposed algorithm can obtain a better reconstruction quality compared to the conventional alternative projection methods, even outperform the recent sparsity-based algorithms in terms of reconstruction quality.
['Baoshun Shi', 'Qiusheng Lian', 'Shuzhen Chen']
I am writing a research paper on a idea Sparse representation utilizing tight frame for phase retrieval
[{"from": "human", "value": "I am writing a research paper on a idea Sparse representation utilizing tight frame for phase retrieval"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  treat the phase retrieval (PR) problem of reconstructing the interest signal from its Fourier magnitude. Since the Fourier phase information is lost, the problem is ill-posed. Several techniques have been used to address this problem by utilizing various priors such as non-negative, support, and Fourier magnitude constraints. Recent methods exploiting sparsity are developed to improve the reconstruction quality. Hover, the previous algorithms of utilizing sparsity prior suffer from either the low reconstruction quality at low oversampled factors or being sensitive to noise. To address these issues,  propose a framework that exploits sparsity of the signal in the translation invariant Haar pyramid (TIHP) tight frame. Based on this sparsity prior,  formulate the sparse representation regularization term and incorporate it into the PR optimization problem.  propose the alternating iterative algorithm for solving the corresponding non-convex problem by dividing the problem into several subproblems.  give the optimal solution to each subproblem, and experimental simulations under the noise-free and noisy scenario indicate that our proposed algorithm can obtain a better reconstruction quality compared to the conventional alternative projection methods, even outperform the recent sparsity-based algorithms in terms of reconstruction quality."}]