Deconvolution

deconvolution(measured, psf; <keyword arguments>)

Computes the deconvolution of measured and psf. Return parameter is a tuple with two elements. The first entry is the deconvolved image. The second return parameter is the output of the optimization of Optim.jl

Multiple keyword arguments can be specified for different loss functions, regularizers and mappings.

Arguments

• loss=Poisson(): the loss function taking a vector the same shape as measured.
• regularizer=nothing: A regularizer function, same form as loss. See GR, TV, Tikhonov and the help page for different regularizers.
• λ=0.05: A float indicating the total weighting of the regularizer with respect to the global loss function
• background=0: A float indicating a background intensity level.
• mapping=Non_negative(): Applies a mapping of the optimizer weight. Default is a parabola which achieves a non-negativity constraint.
• iterations=nothing: Specifies a number of iterations after the optimization. definitely should stop. By default 20 iterations will be selected by generic_invert.jl, if nothing is provided.
• conv_dims: A tuple indicating over which dimensions the convolution should happen. per default conv_dims=1:ndims(psf)
• plan_fft=true: Boolean whether plan_fft is used. Gives a slight speed improvement.
• padding=0: an float indicating the amount (fraction of the size in that dimension) of padded regions around the reconstruction. Prevents wrap around effects of the FFT. A array with size(arr)=(400, 400) with padding=0.05 would result in reconstruction size of (440, 440). However, if padding is >= 0.0, we only return the reconstruction cropped to the original size. For negative paddings, the absolute value is used, but the result maintains the padded size. padding=0 disables any padding.
• opt_package=Opt_Optim: decides which backend for the optimizer is used.
• opt=LBFGS(): The chosen optimizer which must fit to opt_package
• opt_options=nothing: Can be a options file required by Optim.jl. Will overwrite iterations.
• initial=mean(measured): defines a value (or array) with the initial guess. This will be pulled through the inverse mapping function and extended with a mean value (if border regions are used).
• debug_f=nothing: A debug function which must take a single argument, the current reconstruction.

Example

julia> using DeconvOptim, TestImages, Colors, Noise;

julia> img = Float32.(testimage("resolution_test_512"));

julia> psf = Float32.(generate_psf(size(img), 30));

julia> img_b = conv(img, psf);

julia> img_n = poisson(img_b, 300);

julia> res, o = deconvolution(img_n, psf);

richardson_lucy_iterative(measured, psf; <keyword arguments>)

Classical iterative Richardson-Lucy iteration scheme for deconvolution. measured is the measured array and psf the point spread function. Converges slower than the optimization approach of deconvolution

Keyword Arguments

• regularizer=GR(): A regularizer function. Can be exchanged
• λ=0.05: A float indicating the total weighting of the regularizer with respect to the global loss function
• iterations=100: Specifies number of iterations.
• progress: if not nothing, the progress will be monitored in a summary dictionary as obtained by DeconvOptim.optionstracedeconv()

Example

julia> using DeconvOptim, TestImages, Colors, Noise;

julia> img = Float32.(testimage("resolution_test_512"));

julia> psf = Float32.(generate_psf(size(img), 30));

julia> img_b = conv(img, psf);

julia> img_n = poisson(img_b, 300);

julia> @time res = richardson_lucy_iterative(img_n, psf);

invert(measured, rec0, forward; <keyword arguments>)

Tries to invert the forward model. forward is a function taking an input with the shape of rec0 and returns an object which has the same shape as measured

Multiple keyword arguments can be specified for different loss functions, regularizers and mappings.

Arguments

• loss=Poisson(): the loss function being compatible to compare with measured.
• regularizer=nothing: A regularizer function, same form as loss.
• λ=0.05: A float indicating the total weighting of the regularizer with respect to the global loss function
• mapping=Non_negative(): Applies a mapping of the optimizer weight. Default is a parabola which achieves a non-negativity constraint.
• iterations=nothing: Specifies a number of iterations after the optimization. definitely should stop. Will be overwritten if opt_options is provided. Default: 20
• opt_package=Opt_Optim: decides which backend for the optimizer is used.
• opt=LBFGS(): The chosen optimizer which must fit to opt_package.
• opt_options=nothing: Can be a options file required by Optim.jl. Will overwrite iterations.
• debug_f=nothing: A debug function which must take a single argument, the current reconstruction.