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Mathematics for multimedia signal processing, II

Paulo Ferreira
Universidade de Aveiro

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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