Wavelet bi-frames with uniform symmetry for curve multiresolution processing
Journal of Computational and Applied Mathematics
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
Journal of Computational and Applied Mathematics
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Correspondence between frame shrinkage and high-order nonlinear diffusion
Applied Numerical Mathematics
SIAM Journal on Imaging Sciences
Hybrid regularization image deblurring in the presence of impulsive noise
Journal of Visual Communication and Image Representation
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In infrared astronomy, an observed image from a chop-and-nod process can be considered as the result of passing the original image through a high-pass filter. Here we propose a restoration algorithm which builds up a tight framelet system that has the high-pass filter as one of the framelet filters. Our approach reduces the solution of restoration problem to that of recovering the missing coefficients of the original image in the tight framelet decomposition. The framelet approach provides a natural setting to apply various sophisticated framelet denoising schemes to remove the noise without reducing the intensity of major stars in the image. A proof of the convergence of the algorithm based on convex analysis is also provided. Simulated and real images are tested to illustrate the efficiency of our method over the projected Landweber method.