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