Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision, and biomedical imaging. One of the main challenges in performing this task is to design efficient numerical algorithms to approximate integral operators.  introduce a new method based on a sparse approximation of the blurring operator in the wavelet domain. This method requires $\mathcal{O}(N \epsilon^{-d/M})$ operations to provide $\epsilon$-approximations, where $N$ is the number of pixels of a $d$-dimensional image and $M\geq 1$ is a scalar describing the regularity of the blur kernel. In addition,  propose original methods to define sparsity patterns when only the operator regularity is known. Numerical experiments reveal that our algorithm provides a significant improvement compared to standard methods based on windod convolutions.
['Paul Escande', 'Pierre Weiss']
I am writing a research paper on a idea Sparse Wavelet Representations of Spatially Varying Blurring Operators
[{"from": "human", "value": "I am writing a research paper on a idea Sparse Wavelet Representations of Spatially Varying Blurring Operators"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision, and biomedical imaging. One of the main challenges in performing this task is to design efficient numerical algorithms to approximate integral operators.  introduce a new method based on a sparse approximation of the blurring operator in the wavelet domain. This method requires $\\mathcal{O}(N \\epsilon^{-d/M})$ operations to provide $\\epsilon$-approximations, where $N$ is the number of pixels of a $d$-dimensional image and $M\\geq 1$ is a scalar describing the regularity of the blur kernel. In addition,  propose original methods to define sparsity patterns when only the operator regularity is known. Numerical experiments reveal that our algorithm provides a significant improvement compared to standard methods based on windod convolutions."}]