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A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions (1999)
| Content Provider | CiteSeerX |
|---|---|
| Author | Tang, Wun-Cheung Ng, Michael K. Chan, Raymond H. |
| Abstract | Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for 1-dimensional problems and blockToeplitz -Toeplitz-block matrices for 2-dimensional cases. They are computationally intensive to invert especially in the block case. If the periodic boundary condition is used, the matrices become (block) circulant and can be diagonalized by discrete Fourier transform matrices. In this paper, we consider the use of the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary). The resulting matrices are (block) Toeplitzplus -Hankel matrices. We show that for symmetric blurring functions, these blurring matrices can always be diagonalized by discrete cosine transform matrices. Thus the cost of inversion is significantly lower than that of using the zero or periodic boundary conditions. We also s... |
| File Format | |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Toeplitz Matrix Neumann Boundary Condition Fast Algorithm Resulting Matrix 2-dimensional Case Toeplitzplus Hankel Matrix Discrete Cosine Transform Matrix Block Case Important Problem Dark Background Image Processing Toeplitz-block Matrix Blur Removal 1-dimensional Problem Discrete Fourier Transform Matrix Deblurring Model Symmetric Blurring Function Blurring Matrix Periodic Boundary Condition Original Scene Boundary Condition |
| Content Type | Text |
