RMLImaging

AbstractFourierTransform

Abstract type for Fourier Transform Operators.

AbstractImageModel

Mandatory fields

Optional methods

Mandatory methods

Optional methods

AbstractRegularizer

Mandatory fields

• hyperparameter::Number: the hyper parameter of the regularization function. In default, it should be a number.
• domain::RegularizerDomain: the domain of the image space where the regularization function will be computed.

Mandatory methods

• evaluate(::AbstractRegularizerDomain, ::AbstractRegularizer, ::AbstractImageModel, ::AbstractArray): Evaluate the regularization function for the given input sky image.
• evaluate(::AbstractRegularizer, ::AbstractImageModel, ::AbstractArray): Evaluate the regularization function for the given input sky image.
• cost(::AbstractRegularizer, ::AbstractImageModel, ::AbstractArray): Evaluate the cost function for the given input sky image. The cost function is defined by the product of its hyperparameter and regularization function.
• ``

Abstract type for uv-coverages.

FourierTransform2D <: AbstractFourierTransform

Abstract type for Fourier Transform Operators of a single 2D image.

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().

L1Norm <: AbstractRegularizer

Regularizer using the l1-norm.

fields

• hyperparameter::Number: the hyperparameter of the regularizer
• weight: the weight of the regularizer, which could be a number or an array.
• domain::AbstractRegularizerDomain: the image domain where the regularization funciton will be computed. L1Norm can be computed only in LinearDomain().

SingleNFFT2D(nfft_fwd, nfft_adj, vnorm) <: FourierTransform2D

A Fourier Transform Operator of a single 2D Image using NFFT.

Fields

• nfft_fwd: NFFT operator for the forward transform
• nfft_adj: NFFT operator for the adjoint transform
• Vkernel: the factor (phase shift, pulse funciton, kernel, etc) to be multipled by the forward-transformed visibilities.

SingleUVCoverage(u, v, reverse_idx) <: AbstractUVCoverage

A basic type for single uv-coverage.

Arguemnts:

• u::Vector
• v::Vector
• reverse_idx::Vector

TSV <: AbstractRegularizer

Regularizer using the Istropic Total Squared Variation

fields

• hyperparameter::Number: the hyperparameter of the regularizer
• weight: the weight of the regularizer, which may be used for multi-dimensional images.
• domain::AbstractRegularizerDomain: the image domain where the regularization funciton will be computed.

TV <: AbstractRegularizer

Regularizer using the Istropic Total Variation

fields

• hyperparameter::Number: the hyperparameter of the regularizer
• weight: the weight of the regularizer, which may be used for multi-dimensional images.
• domain::AbstractRegularizerDomain: the image domain where the regularization funciton will be computed.

map!(image::EHTImages.AbstractEHTImage, imager::Imager2D, x::AbstractArray[, idx])

map(image::EHTImages.AbstractEHTImage, imager::Imager2D, x::AbstractArray[, idx])

ImagingProblem(imager::Imager2D, x0::AbstractArray)

Initialize Optimization.OptimizationProblem for RML Imaging. Returns the initialized Optimization.OptimizationProblem object.

Arguments

• imager::Imager2D: the imager
• x0::AbstractArray: the initial image in the parameter domain.

ImagingProblem(imager::Imager2D, initialimage::AbstractEHTImage)

Initialize Optimization.OptimizationProblem for RML Imaging. Returns the initialized Optimization.OptimizationProblem object.

Arguments

• imager::Imager2D: the imager
• x0::AbstractArray: the initial image in the parameter domain.

cost(reg::AbstractRegularizer, skymodel::AbstractImageModel, x::AbstractArray)

Compute the cost function of the given regularization function for the given image parameters on the given image model. In default, this should return reg.hyperparameter .* evaluate(reg, skymodel, x).

Arguments

• reg::AbstractRegularizer: the regularization function.
• skymodel::AbstractImageModel: the model of the input image
• x::AbstractArray: the parameters of the input image

domain(reg::AbstractRegularizer) = reg.domain

Return the computing domain of the given regularizer.

evaluate(imager::Imager2D, x::AbstractArray)

Evaluate chisquares and regularizers from the input image parameters

Arguments

• imager::Imager2D: RML Imaging Setting
• x::AbstractArray: the image parameters

evaluate(imager::Imager2D, image::AbstractEHTImage)

Evaluate chisquares and regularizers from the input image

Arguments

• imager::Imager2D: RML Imaging Setting
• image::AbstractEHTImage: the image

evaluate(::AbstractRegularizer, skymodel::AbstractImage2DModel, x::AbstractArray)

evaluate(reg::AbstractRegularizer, skymodel::AbstractImageModel, x::AbstractArray)

Compute the value of the given regularization function for the given image parameters on the given image model. In default, return evaluate(domain(reg), reg, skymodel, x).

Arguments

• reg::AbstractRegularizer: the regularization function.
• skymodel::AbstractImageModel: the model of the input image
• x::AbstractArray: the parameters of the input image

evaluate(domain::AbstractRegularizerDomain, reg::AbstractRegularizer, skymodel::AbstractImageModel, x::AbstractArray)

Compute the value of the given regularization function for the given image parameters on the given image model. In default, return 0.

Arguments

• domain::AbstractRegularizerDomain: the domain of the image where the regularization function will be computed.
• reg::AbstractRegularizer: the regularization function.
• skymodel::AbstractImageModel: the model of the input image
• x::AbstractArray: the parameters of the input image

hyperparameter(reg::AbstractRegularizer) = reg.hyperparameter

Return the hyperparameter of the given regularizer.

klentropy_base(x::AbstractArray, p::AbstractArray)

Base function of the l1norm.

Arguments

• I::AbstractArray: the image

l1norm(I::AbstractArray, w::Number)

Base function of the l1norm.

Arguments

• I::AbstractArray: the image
• w::Number: the regularization weight

l1norm(I::AbstractArray)

Base function of the l1norm.

Arguments

• I::AbstractArray: the image

lossfunc(x, imager::Imager2D)

The Loss function for the basic 2-dimensional RML Imaging problem. Returns the cost function.

Arguments

• x::AbstractArray: the image parameters
• imager::Imager2D: RML Imaging Setting

transform_linear_forward(model::AbstractImageModel, x::AbstractArray)

Convert the input array of the image model parameters into the corresponding array of the linear-scale intensity map. This is supposed to be the inverse funciton of $transform_linear_inverse$.

Arguments

• model::AbstractImageModel: the image model
• x::AbstractArray: the array of the image model parameters

transform_linear_forward(model::AbstractImageModel, x::AbstractArray)

Convert the input array of the linear-scale intensity map into the array of the corresponding model parameters. This is supposed to be the inverse funciton of $transform_linear_forward$.

Arguments

• model::AbstractImageModel: the image model
• x::AbstractArray: the array of the linear-scale intensity map

tsv_base(I::AbstractArray, w::Number; ex::Floop's Executor)

Base function of the istropic total squared Variation.

Arguments

• I::AbstractArray: the input two dimensional real image
• w::Number: the regularization weight

tsv_base(I::AbstractArray; ex::FLoops's Executor)

Base function of the istropic total squared Variation.

Arguments

• I::AbstractArray: the input two dimensional real image

tsv_base_grad_pixel(I::AbstractArray, ix::Integer, iy::Integer)

Return the gradient of the squared variation for the given pixel.

tsv_base_pixel(I::AbstractArray, ix::Integer, iy::Integer)

Return the squared variation for the given pixel.

tv_base(I::AbstractArray, w::Number; ex::FLoops's Executor)

Base function of the istropic total variation.

Arguments

• I::AbstractArray: the input two dimensional real image
• w::Number: the regularization weight

tv_base(I::AbstractArray; ex::FLoops's Executor)

Base function of the istropic total variation.

Arguments

• I::AbstractArray: the input two dimensional real image

tv_base_pixel(I::AbstractArray, ix::Integer, iy::Integer)

Evaluate the gradient of the istropic variation term for the given pixel.

tv_base_pixel(I::AbstractArray, ix::Integer, iy::Integer)

Evaluate the istropic variation term for the given pixel.