Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  considers the problem of recovering a group sparse signal matrix $\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corrupted measurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots, \mathbf{A}_{(L)}\mathbf{y}_{L}] + \mathbf{S}$, where $\mathbf{A}_{(i)}$'s are known sensing matrices and $\mathbf{S}$ is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover $\mathbf{Y}$ and $\mathbf{S}$ through simultaneously minimizing the $\ell_{2,1}$-norm of $\mathbf{Y}$ and the $\ell_1$-norm of $\mathbf{S}$ under the measurement constraints.  prove that $\mathbf{Y}$ and $\mathbf{S}$ can be exactly recovered from the RGL model with a high probability for a very general class of $\mathbf{A}_{(i)}$'s.
['Xiaohan Wei', 'Qing Ling', 'Zhu Han']
I am writing a research paper on a idea Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso
[{"from": "human", "value": "I am writing a research paper on a idea Recoverability of Group Sparse Signals from Corrupted Measurements via Robust Group Lasso"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  considers the problem of recovering a group sparse signal matrix $\\mathbf{Y} = [\\mathbf{y}_1, \\cdots, \\mathbf{y}_L]$ from sparsely corrupted measurements $\\mathbf{M} = [\\mathbf{A}_{(1)}\\mathbf{y}_{1}, \\cdots, \\mathbf{A}_{(L)}\\mathbf{y}_{L}] + \\mathbf{S}$, where $\\mathbf{A}_{(i)}$'s are known sensing matrices and $\\mathbf{S}$ is an unknown sparse error matrix. A robust group lasso (RGL) model is proposed to recover $\\mathbf{Y}$ and $\\mathbf{S}$ through simultaneously minimizing the $\\ell_{2,1}$-norm of $\\mathbf{Y}$ and the $\\ell_1$-norm of $\\mathbf{S}$ under the measurement constraints.  prove that $\\mathbf{Y}$ and $\\mathbf{S}$ can be exactly recovered from the RGL model with a high probability for a very general class of $\\mathbf{A}_{(i)}$'s."}]