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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 j≤d/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, t≤d/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 t≤j<t+τ or j<t+τ−d and M(j,j)=1 else.