Implementation of basis pursuit denoising with StructuredOptimization.jl

optimized_bpdn.jl

using StructuredOptimization

"""
Simple implementation of basis pursuit denoising using StructuredOptimization.jl

INPUT
-----
m, n : Size of the image in both direction.
idx : Linear indices of the measured pixels.
y : Pixel measurements.
λ : (Optional) Sparsity knob.

OUTPUT
------
x : Estimated image.

"""
function bpdn(m, n, idx, y ; λ=0.1)
  # --> Initialize variable.
  x = Variable(eltype(y), m, n)
  # --> Solve the compressed sensing problem.
  @minimize ls(idct(x)[idx] - y) + λ*norm(x, 1)

  return ~x
end