A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...

Real images usually have sparse approximations under some tight frame systems derived from either framelets, over sampled discrete (window) cosine or Fourier transform. In this paper, we propose a method for image deblurring in tight frame domains. It is reduced to finding a sparse solution of a system of linear equations whose coefficients matrix is rectangular. Then, a modified version of the...

Image inpainting is a fundamental problem in image processing and has many applications. Motivated by the recent tight frame based methods on image restoration in either the image or the transform domain, we propose an iterative tight frame algorithm for image inpainting. We consider the convergence of this framelet-based algorithm by interpreting it as an iteration for minimizing a special fun...