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Certain signal reconstruction problems can be understood in terms of frames
and redundant representations. The redundancy is useful because it leads to
robust signal representations, that is, representations in which partial
loss of data can be tolerated without misbehavior or adverse effects. Some
of the methods that can be used to recover from missing data errors are
examined, emphasizing finite-dimensional theory because of its simplicity
and practical usefulness, and interpreting the results in terms of discrete
finite frames. The connection between the frame algorithm and a few other
iterative reconstruction methods, such as POCS and the Papoulis-Gerchberg
iteration, is detailed.
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Advanced Study Institute