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Table 2 Mask models

From: Fast dictionary learning from incomplete data

Erasure model
Our erasure model depends on four parameters,
p 1 - the relative signal corruption of the first half of coordinates,
p 2 - the relative signal corruption of the second half of coordinates,
q 1 - the corruption factor of one half of the signals and
q 2 - the corruption factor of the other half of the signals.
Based on these parameters, we generate a random erasure mask as follows. First, we choose q{q 1,q 2} uniformly at random and determine for every entry the probability of being non-zero as η j =q p 1 for jd/2 and η j =q p 2 for j>d/2. We then generate a mask as a realisation of the independent Bernoulli variables M(j,j)B(η j ), that is P(M(j,j)=1)=η j .
Burst error model
Our burst error model depends on four parameters,
p T - the probability of a burst of length T,
p 2T - the probability of a burst of length 2T,
T - the burst length and
q - the probability of the burst starting in the first half of the coordinates.
Based on these parameters, we generate a burst error mask as follows. First, we choose a burstlength τ{0,T,2T} according to the probability distribution prescribed by {p 0,p T ,p 2T }, where p 0=1−p T p 2T . We then decide according to the probability q whether the burst start t occurs among the first half of coordinates, td/2, or the second half, t>d/2. Finally, we draw the burst start t uniformly at random from the chosen half of coordinates and in a cyclic fashion set M(j,j)=0 whenever tj<t+τ or j<t+τd and M(j,j)=1 else.