GaussMLE.GaussFit

GaussFit

The GaussFit module provides functions for fitting Gaussian models to a 2D box or a stack of 2D "boxes" of data.

The fitstack function is the primary exported function of GaussMLE.jl. It takes in a 3D array containing the data to be fitted, a symbol indicating the type of Gaussian model to fit, and additional model-specific arguments required for fitting. It returns an array of fitted parameters for each 2D box and an array of uncertainties for each set of fitted parameters.

The fitstack function also accepts optional keyword arguments for specifying a camera variance image and the top left corners of the boxes in relation to the variance image. These are used to implement a variance-weighted fit as described by Huang et al:

• Huang, F., Hartwich, T., Rivera-Molina, F. et al. "Video-rate nanoscopy using sCMOS camera–specific single-molecule localization algorithms." Nat Methods 10, 653–658 (2013). DOI: 10.1038/nmeth.2488

Exported Functions

• fitstack: Fit Gaussian models to each box in a stack of 2D "boxes" of data.

Notes

• Data and Variance image must be in units of photons (Poisson distributed).

calclogL(θ::GaussMLEParams{T}, box::AbstractArray{T}, args::GaussMLEArgs) where {T<:Real}

Calculate the log-likelihood of a Gaussian MLE fit for a given set of parameters and data.

Arguments

• θ::GaussMLEParams{T}: A GaussMLEParams object containing the parameters of the Gaussian MLE fit.
• box::AbstractArray{T}: An AbstractArray containing the data to fit.
• args::GaussMLEArgs: A GaussMLEArgs object containing additional arguments for the fit.

Returns

• logL: The log-likelihood of the fit.

crlb!(Σ::GaussMLEΣ{T}, grad_pixel::AbstractArray{T}, θ::GaussMLEParams{T}, boxsize::Int, args::GaussMLEArgs)

Calculate the Cramer-Rao lower bound (CRLB) for a given set of parameters and data.

Arguments

• Σ::GaussMLEΣ{T}: A GaussMLEΣ object to store the CRLB values.
• grad_pixel::AbstractArray{T}: An AbstractArray to store the gradient values.
• θ::GaussMLEParams{T}: A GaussMLEParams object containing the parameters of the Gaussian MLE fit.
• boxsize::Int: The size of the box to fit.
• args::GaussMLEArgs: A GaussMLEArgs object containing additional arguments for the fit.

fitbox!(θ::GaussMLEParams{T}, Σ::GaussMLEΣ{T}, box::AbstractArray{T}, args::GaussMLEArgs,
        varimage::Union{T,AbstractArray{T}}, boxcorners::Union{T,AbstractArray{T}};
        maxiter::Int = 100) where {T<:Real}

Fits a Gaussian blob model using maximum likelihood estimation and Poisson noise model to a single 2D "box" of data.

Arguments

• θ::GaussMLEParams{T}: Initial parameters for the Gaussian MLE model.
• Σ::GaussMLEΣ{T}: Container for the calculated Cramer-Rao Lower Bound (CRLB) and log likelihood.
• box::AbstractArray{T}: 2D array containing the data to be fitted.
• args::GaussMLEArgs: Additional arguments required for fitting.
• varimage::Union{T,AbstractArray{T}}: Camera readnoise variance image, or a single variance for all pixels.
• boxcorners::Union{T,AbstractArray{T}}: The corners of the box in the full image. Used when varimage is an image.

Keyword Arguments

• maxiter::Int: Maximum number of iterations for the fitting process (default is 100).

Output

• Updates θ and Σ in-place with the fitted parameters and their uncertainties.

Notes

• This function performs iterative fitting and stops either when the fit converges or when it reaches maxiter iterations.
• The input box must be a square 2D array.
• Input data box is assumed to be background subtracted.

fitstack(stack::AbstractArray{T}, modelsymbol::Symbol, args::GaussMLEArgs{T}; varimage::Union{T,AbstractArray{T}}=T(0), boxcorners::Union{T,AbstractArray{T}}=T(0)) where T <: Real

Fit Gaussian models to each box in a stack of 2D "boxes" of data.

Arguments

• stack::AbstractArray{T}: 3D array containing the data to be fitted. Each slice along the third dimension is treated as a separate 2D box.
• modelsymbol::Symbol: Symbol indicating the type of Gaussian model to fit.
• args::GaussMLEArgs{T}: Additional model-specific arguments required for fitting.

Keyword Arguments

• varimage::Union{T,AbstractArray{T}}: Camera variance image, or a single variance for all pixels (default is T(0)).
• boxcorners::Union{T,AbstractArray{T}}: The top left corners of the boxes in the variance image (default is T(0)).

Returns

• θ: Array of fitted parameters for each 2D box.
• Σ: Array of uncertainties for each set of fitted parameters.

Notes

• Data and Variance image must be in units of photons (Poisson distributed).

Example

fitstack(stack, :xynb, args; varimage=myvarimage, boxcorners=myboxcorners)