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A sequence in a Hilbert space H is a frame for H if there exist positive constants A and B such that, for every unit x in H, the sum of squares of inner products of x with elements of frames converges to the number between A and B. Frames are often used in process of encoding and decoding signals. It is the redundancy property of frames that makes them useful in applications where some of the coefficients could be lost during the data transmission. We discuss the problem of recovering signal from frame coefficients with erasures. Provided that the erasure set satisfies the minimal redundancy condition, we construct a suitable synthesizing dual frame which enables a perfect reconstruction of the original signal without recovering the lost coefficients. This is a joint work with Damir Bakić.
Hilbert space ; frame ; dual frame
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