Operators and Norms involved in the formulation of variational imaging problems. It is an extension of the StructuredOptimization julia module, designed to support bilevel programming problems

To install the package, hit ] from the Julia command line to enter the package manager, then

pkg> add BilevelImagingParameterLearning

These are a set of norms used for imaging models, in particular:

1. Scalar Total Variation (TV)
2. Scale-Dependent Total Variation (SD-TV)
3. Piecewise-Constant Total Variation (PC-TV)
4. Generalized Total Variation (TGV)

These are a set of operators used for imaging models, in particular:

1. SecondOrderVariation
2. FFT

With using BilevelImagingParameterLearning the package exports the eval and eval! methods to evaluate an argument, conj and conj! methods to evaluate the conjugated mapping of several inputs.

For example, you can create the L1-norm as follows.

julia> f = NormL1(3.5)
description : weighted L1 norm
type        : Array{Complex} → Real
expression  : x ↦ λ||x||_1
parameters  : λ = 3.5

Functions created this way are, of course, callable.

julia> x = randn(10) # some random point
julia> f(x)
32.40700818735099

1. De Los Reyes, Villacis, "Bilevel Scale Dependent ROF Parameter Learning", XXX