A Primer for Undergraduate Research by Aaron Wootton Valerie Peterson & Christopher Lee

Author:Aaron Wootton, Valerie Peterson & Christopher Lee
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

If one of the coefficients, say the second coefficient is lost, then at the reconstruction stage one gets

and the error in the reconstruction is

where ∥. ∥2 is the Euclidean distance in Instead of an ONB, let us now use the redundant set

See Figure 1(a). In terms of this set, the vector (1, 1) can be written as

If the coefficient corresponding to f 0 is lost then one obtains

and the reconstruction error is

which is less than the error when the first coefficient was lost while using the standard ONB of Losing a single coefficient with an ONB in can be thought of as losing 50% of the coefficients. In the case of the redundant set under consideration suppose that 50%, that is, three coefficients are lost. If they are the first three, then the reconstructed vector is

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