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- W2469961892 abstract "The purpose of this chapter is to give a detailed tutorial-style exposition of a method we have recently discovered for complete recovery from frame and sampling erasures by inverting a matrix of dimension the cardinality of the erasure set. This is usually simpler and more efficient than inverting the frame operator of the remaining coefficients because the erasure set is usually much smaller than the dimension of the space. The method is not hard and can be easily implemented on a computer, even for infinite frames and sampling schemes as long as one is dealing with only a finite set of erasures. The set of erasures that can be handled in this way can be very large. We call the method nilpotent bridging. We introduced this method in a recent research article, along with some new classification results and methods of measuring redundancy that are based on the matricial infrastructure of a dual frame pair: the set of all submatrices of the cross-Gramian of the pair. The first author gave a talk on this material in a conference at Vanderbilt University in May 2014 entitled “Building bridges (reconstruction from frame and sampling omissions)”, and this chapter is based on the notes from that talk. In the process of developing the mathematics underlying the bridging technique, we discovered a second method for recovery from erasures in finitely many steps, and this chapter will also discuss this alternate method." @default.
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- W2469961892 date "2015-01-01" @default.
- W2469961892 modified "2023-09-26" @default.
- W2469961892 title "Bridging erasures and the infrastructure of frames" @default.
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- W2469961892 doi "https://doi.org/10.1007/978-3-319-20188-7_2" @default.
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