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loiseaujc/basis_pursuit_denoising.jl

Last active February 17, 2021 14:03
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basis_pursuit_denoising.jl
using StructuredOptimization
"""
Simple implementation of basis pursuit denoising using StructuredOptimization.jl
INPUT
-----
C : The measurement matrix.
Ψ : Basis in which x is assumed to be sparse.
y : Pixel measurements.
λ : (Optional) Sparsity knob.
OUTPUT
------
x : Estimated image.
"""
function bpdn(C, Ψ, y ; λ=0.1)
# --> Initialize variable.
x = Variable(eltype(y), size(Ψ, 2))
# --> Solve the compressed sensing problem.
@minimize ls(C * Ψ * x - y) + λ*norm(x, 1)
return ~x
end
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