Feasibility Pump Algorithm for Sparse Representation under Laplacian Noise

Algorithm 1

Sparse feasibility pump: SFP uses (4) and (5); SFPreg uses (9) and (10).

Data: Dictionary , signal to represent , sparsity level , maximum number of iterations ,

weight parameters , , (the latter for SFPreg only)

Result: a feasible solution

Solve (4)/(9) for using a linear programming solver

Use rounding procedure to obtain vector

while number of iterations ≤ Iter do

Solve the problem (5)/(10) for the vectors and

if is integer then

return

end

Use rounding procedure to obtain vector

if cycle is detected then

Use perturbation (7) on

end

Update the value of using (6)

end