Foundations and Trends in Signal Processing
Systematic construction of real lapped tight frame transforms
IEEE Transactions on Signal Processing
Frame-theoretic analysis of robust filter bank frames to quantization and erasures
IEEE Transactions on Signal Processing
Orthogonal projection decomposition of matrices and construction of fusion frames
Advances in Computational Mathematics
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Motivated by the use of frames for robust transmission over the Internet, we present a first systematic construction of real tight frames with maximum robustness to erasures. We approach the problem in steps: we first construct maximally robust frames by using polynomial transforms. We then add tightness as an additional property with the help of orthogonal polynomials. Finally, we impose the last requirement of equal norm and construct, to our best knowledge, the first real, tight, equal-norm frames maximally robust to erasures.