VLBISkyRegularizers.jl

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VLBISkyRegularizers API ​

Index ​

Regularizers ​

# VLBISkyRegularizers.AbstractRegularizer — Type.
julia
AbstractRegularizer

Used to define the regularizer functions. See subtypes(AbstractRegularizer) for a list of implemented regularizers.

Mandatory fields

  • hyperparameter::Number: the hyperparameter of the regularization function.

  • image_domain::AbstractDomain: the domain of the image space

  • evaluation_domain::AbstractDomain: the domain on which the regularizer is to be evaluated

  • grid: grid on which image is defined

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# VLBISkyRegularizers.AddRegularizer — Type.
julia
AddRegularizer{R1<:AbstractRegularizer, R2<:AbstractRegularizer} <: AbstractRegularizer

Structure for adding two regularizers.

The two regularizers must have the same grid and image domain.

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# VLBISkyRegularizers.L1 — Type.
julia
L1 <: AbstractRegularizer

Regularizer using the L1 norm.

fields

  • hyperparameter::Number: the hyperparameter of the regularization function.

  • image_domain::AbstractDomain: the domain of the image space

  • evaluation_domain::AbstractDomain: the domain on which the regularizer is to be evaluated

  • grid: grid on which image is defined

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# VLBISkyRegularizers.TSV — Type.
julia
TSV <: AbstractRegularizer

Regularizer using the Isotropic Total Squared Variation.

fields

  • hyperparameter::Number: the hyperparameter of the regularization function.

  • image_domain::AbstractDomain: the domain of the image space

  • evaluation_domain::AbstractDomain: the domain on which the regularizer is to be evaluated

  • grid: grid on which image is defined

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# VLBISkyRegularizers.TV — Type.
julia
TV <: AbstractRegularizer

Regularizer using the Isotropic Total Variation.

fields

  • hyperparameter::Number: the hyperparameter of the regularization function.

  • image_domain::AbstractDomain: the domain of the image space

  • evaluation_domain::AbstractDomain: the domain on which the regularizer is to be evaluated

  • grid: grid on which image is defined

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# VLBISkyRegularizers.WaveletL1 — Type.
julia
WaveletL1 <: AbstractRegularizer

Regularizer using the l1-norm with a wavelet transform

fields

  • hyperparameter::Number: the hyperparameter of the regularization function.

  • image_domain::AbstractDomain: the domain of the image space

  • evaluation_domain::AbstractDomain: the domain on which the regularizer is to be evaluated

  • wavelet::WVType: wavelet type

  • grid: grid on which image is defined

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# VLBISkyRegularizers.WeightRegularizer — Type.
julia
WeightRegularizer{R<:AbstractRegularizer, W<:Number} <: AbstractRegularizer

Structure for weighting a regularizer by a scalar.

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# VLBISkyRegularizers.WVType — Type.
julia
WVType

Wavelet type used for Wavelet Transform L1 Regularizer. By default, this is the full Daubechies 2 wavelet.

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# VLBISkyRegularizers.KLE — Type.
julia
KLEntropy <: AbstractRegularizer

Regularizer using the Kullback-Leibler divergence (or a relative entropy)

fields

  • hyperparameter::Number: the hyperparameter of the regularizer

  • prior: the prior image

  • domain::AbstractRegularizerDomain: the image domain where the regularization funciton will be computed. KLEntropy can be computed only in LinearDomain().

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Domains ​

# VLBISkyRegularizers.AbstractDomain — Type.
julia
AbstractDomain

Used to define the image and evaluation domains.

See subtypes(AbstractDomain) for a list of possible domains.

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# VLBISkyRegularizers.ALRDomain — Type.
julia
ALRDomain

Additive Log-Ratio transform. Can only be used as an image domain.

Image transformation is the inverse ALR function. Similar to softmax but treats one pixel (the last pixel) as special.

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# VLBISkyRegularizers.CLRDomain — Type.
julia
CLRDomain

Centered Log-Ratio transformation. Can only be used as an image domain.

Image transformation is the softmax function (applies the exponential function and normalizes by the sum).

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# VLBISkyRegularizers.LinearDomain — Type.
julia
LinearDomain

Can be used as an image and evaluation domain.

No transformation in evaluation. Image simplex transformation normalizes the image by the sum and absolute value.

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# VLBISkyRegularizers.LogDomain — Type.
julia
LogDomain

Can be used as an image and evaluation domain.

Logarithmic transformation in evaluation. Image transformation is the softmax function (applies the exponential function and normalizes by the sum).

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# VLBISkyRegularizers.ParameterDomain — Type.
julia
ParameterDomain

Can only be used as an evaluation domain.

Sets the evaluation domain equal to the image domain.

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Functions ​

# VLBISkyRegularizers.evaluate — Function.
julia
evaluate(::AbstractRegularizer, ::AbstractArray)

Compute the value of the given regularization function on the input image. By default, return 0.

source

julia
evaluate(reg::L1, x::AbstractArray)

Evaluate the L1 norm regularizer at an image.

Arguments

  • reg::L1: L1 norm regularizer

  • x::AbstractArray: the image

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julia
evaluate(reg::TV, x::AbstractArray)

Evaluate the TV regularizer at an image.

Arguments

  • reg::TV: TV regularizer

  • x::AbstractArray: the image

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julia
evaluate(reg::TSV, x::AbstractArray)

Evaluate the TSV regularizer at an image.

Arguments

  • reg::TSV: TSV regularizer

  • x::AbstractArray: the image

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# VLBISkyRegularizers.evaluation_domain — Function.
julia
evaluation_domain(reg::AbstractRegularizer)

Return the evaluation domain of the given regularizer.

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# VLBISkyRegularizers.grid — Function.
julia
grid(reg::AbstractRegularizer)

Return the grid on which an image to be regularized is defined.

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# VLBISkyRegularizers.image_domain — Function.
julia
image_domain(reg::AbstractRegularizer)

Return the image domain of the given regularizer.

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# VLBISkyRegularizers.regularizers — Function.
julia
regularizers(::AbstractRegularizer)

List regularizers used.

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# VLBISkyRegularizers.solve_opt — Function.
julia
solve_opt(post::VLBIPosterior, opttype=Optimisers.Adam(), adtype=Optimization.AutoEnzyme(); ntrials=5, maxiters=10_000, init_params=nothing, verbose=false, stride=1000)

Solve for the MAP of post using the opttype optimizer.

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# VLBISkyRegularizers.transform_domain — Function.
julia
transform_domain(ImageDomain::AbstractDomain, EvaluationDomain::AbstractDomain, x::AbstractArray)

Transform an array from the image domain to the evaluation domain.

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# VLBISkyRegularizers.transform_image — Function.
julia
transform_image(::AbstractDomain, x::AbstractArray)

Transform an array to the normalized, non-negative image simplex domain.

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# VLBISkyRegularizers.transform_linear — Function.
julia
transform_linear(::AbstractDomain, x::AbstractArray)

Transform an array to the linear domain.

Same as transform_image but does not necessarily impose non-negativity and normalization.

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# Distributions._logpdf — Function.
julia
Distributions._logpdf(d::Regularizers, image::AbstractMatrix{<:Real})

The log density of the regularizers evaluated at the input image. .

Arguments

  • reg::Regularizers: the regularizer functions.

  • image::AbstractMatrix{<:Real}: the model of the input image

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# Distributions._rand! — Function.
julia
Distributions._rand!(rng::Random.AbstractRNG, ::Regularizers, x::AbstractMatrix)

Return a random sample of shape equal to the shape of the input matrix

Arguments

  • rng::Random.AbstractRNG: an RNG seed object

  • ::Regularizers: any set of regularizer functions

  • x::AbstractMatrix: input matrix

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# VLBISkyRegularizers.l1_base — Function.
julia
l1_base(x::AbstractArray)

Base function of the L1 norm.

Arguments

  • x::AbstractArray: the image

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julia
l1_base(x::AbstractArray, w::Number)

Base function of the L1 norm.

Arguments

  • x::AbstractArray: the image

  • 'w::Number' : the regularization weight

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# VLBISkyRegularizers.tv_base — Function.
julia
tv_base(x::AbstractArray)

Base function of the isotropic total variation.

Arguments

  • x::AbstractArray: the image

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julia
tv_base(x::AbstractArray, w::Number)

Base function of the isotropic total variation.

Arguments

  • x::AbstractArray: the image

  • 'w::Number' : the regularization weight

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# VLBISkyRegularizers.wavelet_transform — Function.
julia
wavelet_l1_base(x::AbstractArray, wv::WaveletL1)

Base function of the Wavelet L1 norm.

Arguments

  • x::AbstractArray: the image

  • wv::WVType : the wavelet transform type

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# VLBISkyRegularizers.tsv_base — Function.
julia
tsv_base(x::AbstractArray)

Base function of the isotropic total squared variation.

Arguments

  • x::AbstractArray: the image

source

julia
tsv_base(x::AbstractArray, w::Number)

Base function of the isotropic total squared variation.

Arguments

  • x::AbstractArray: the image

  • 'w::Number' : the regularization weight

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# VLBISkyRegularizers.klentropy_base — Function.
julia
klentropy_base(x::AbstractArray, p::AbstractArray)

Base function of the KL-Entropy norm.

Arguments

  • I::IntensityMap: the image

  • p::IntensityMap: the prior image

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