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juliacon_2021.jl
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### A Pluto.jl notebook ###
# v0.14.5
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
el
end
end
# ╔═╡ 0507f8ed-8b64-48af-a6c4-ff7c4211b9e9
begin
using Pkg
Pkg.activate(".")
end
# ╔═╡ 3310d2f7-450a-4cd1-9c3a-46d02d23a7c6
using Revise
# ╔═╡ d27b2d72-d264-11eb-0be5-13dcacfd2adc
using DeconvOptim, TestImages, ImageShow, Plots, LinearAlgebra, IndexFunArrays, Noise, FourierTools, SpecialFunctions, FFTW, LaTeXStrings, PlutoUI, Images, Tullio
# ╔═╡ 952b251c-207b-4412-b6e1-268fce1647d9
begin
img = Float32.(testimage("fabio_gray"));
img_1D = img[:, 200]
end;
# ╔═╡ fa8cd9c9-a2fd-495c-8d22-ada7bb9c39f6
otf(x, Δx=1) = begin
x = abs(x)
if x <= Δx
SpecialFunctions.jinc(x * Δx *(1-x/Δx)) .* 2 / π * (acos(x/Δx) - x/Δx * sqrt(1-(x/Δx)^2))
else
zero(x)
end
end
# ╔═╡ 9a07bc88-be76-4531-bc91-df0d20c3221c
begin
x = range(-1.5, 1.5, length=size(img, 1))
freqs = fftshift(fftfreq(size(img_1D, 1), 1))
psf = Float32.(DeconvOptim.generate_psf(size(img), 20))
psf_1D = psf[1, :]
psf_1D ./= sum(psf_1D)
otf_1D = abs.(ffts(psf_1D))
end;
# ╔═╡ 24fc86da-0b7c-493c-8977-2a19ef6dc133
img_n = Float32.(poisson(DeconvOptim.conv(img, psf), 1000));
# ╔═╡ 3bda922d-552b-42ec-9055-33a141b5841a
blur(x, otf=otf_1D) = iffts(ffts(x) .* otf)
# ╔═╡ 308e2562-5a20-4082-8a6d-9fb135738c49
md"
Mathematically:
$(S * \text{PSF})(\mathbf r) = \int_{-\infty}^{\infty} S(\mathbf r - \mathbf x) \cdot \text{PSF}(\mathbf x) \, \mathrm d \mathbf x$
"
# ╔═╡ b542187a-3ae7-4430-a81d-f968d9000427
img_blurry = DeconvOptim.conv(img, psf);
# ╔═╡ 88d83629-f1b2-4d69-928f-d4acfbc76b70
reg_1D = TV(num_dims=1);
# ╔═╡ d6d0f436-48fd-4e8a-863c-3e9d3850cc91
begin
reg_tik = Tikhonov()
reg_TV = TV()
reg_GR = DeconvOptim.GR()
end
# ╔═╡ 061faf49-662c-4508-83b4-ddcf0970ed0d
md"### DeconvOptim.jl: Microscopy Image Deconvolution
"
# ╔═╡ 23829201-9756-4ef8-90c9-3917b761fe4b
load("../docs/src/assets/logo.png")
# ╔═╡ 30f21bb8-6d09-4fce-9d2a-568bfaf3ff7a
md"
* **Felix Wechsler:** Master Student at the Leibniz Institute of Photonic Technology in Jena, Germany
* https://github.com/roflmaostc/DeconvOptim.jl
* `]add DeconvOptim`
"
# ╔═╡ 7a0a44c9-fb07-44e6-9a8b-8f720b84e6f6
md"""### Image Convolution
* Typical description of isotropic blur of an image
* The blurring kernel describes blur
* In optics/microscopy a finite sized dot called Point Spread Function (**PSF**)
* often a Gaussian function used in image processing
* cigarre shaped object for motion blur
Discrete version:
$(S * \text{PSF})[i] = \sum_{m} S[i-m] \cdot \text{PSF}[m]$
"""
# ╔═╡ 49686d9a-1683-428f-83ba-a9131c2ad432
[Gray.(img) Gray.(DeconvOptim.conv(img, psf))]
# ╔═╡ 491ec7cb-1663-4acf-b81f-9acafba2b63d
md"## Convolution Theorem
$(S * \text{PSF})(\mathbf r) = \mathcal{F}^{-1}\bigg[ \mathcal{F}[S] \cdot \mathcal{F}[\text{PSF}] \bigg]$
* we can express the convolution with a Fast Fourier Transform (FFT) which only takes $\mathcal O(N \log(N))$ operations
* For large kernels (especially in 3D), sliding kernels are slower
* $\mathcal{F}[\text{PSF}]$ is called the $\text{OTF}$
"
# ╔═╡ b6f9e42e-5a23-40ad-9e73-8f02da48f69c
md"### Optical System act as low pass filter
* $\text{OTF}$ shows the frequency throughput
"
# ╔═╡ e31f4704-5bce-4c8d-b3a7-873a3460d9f8
plot(x, otf.(x), xlabel="frequency / maximum frequency", ylabel="contrast")
# ╔═╡ dc8cf4e2-a87c-47ea-8247-3ae772852241
md"## Frequency spectrum of blurred sample $Y(\mathbf r)$
Blurred sample:
$Y(\mathbf r) = (S * \text{PSF})(\mathbf r)$
"
# ╔═╡ f8033d13-faee-41f5-bdd6-ae8721e8b8a8
begin
plot(freqs, abs.(ffts(img_blurry)[:, 128]), yaxis=:log, ylabel="real part of FFT output in AU", xlabel="frequency in 1/px", ylims=(1e-4, 1e2), label="blurred")
plot!(freqs, abs.(ffts(img)[:, 128]), ylabel="abs of FFT output in AU",
xlabel="frequency in 1/px", yaxis=:log,
ylims=(1e-4, 1e4), label="ground truth")
#plot!(freqs, abs.(ffts(DeconvOptim.conv(img_1D, psf_1D))))
end
# ╔═╡ fe7e0292-31f6-43b5-83a5-a38698a87563
md"## Deconvolution Pipeline
* based on:
* Zygote.jl
* Optim.jl
* Tullio.jl
* CUDA.jl
"
# ╔═╡ e9ef5ba4-56c0-4595-bc28-e04882f44a9a
load("../docs/src/assets/tex/pipeline.png")
# ╔═╡ 90e5708c-05a4-46e4-b1e4-9a61c96dae32
TV_by_hand(x) = @tullio r = sqrt(1f-8 + abs2(x[i, j] - x[i+1, j]) +
abs2(x[i, j] - x[i, j+1]))
# ╔═╡ 03139ac5-3525-4fad-abf1-84421492b763
DeconvOptim.generate_TV(4, [1,2, 3], [1,1, 1], 1, 0)[1]
# ╔═╡ 4e84e739-9c59-4939-8b04-aec7dc069d67
md"
### Deconvolve with DeconvOptim.jl
"
# ╔═╡ 9d9a5da2-14df-46e6-b7e6-5a33aade1754
@bind reg_list2 Select(["1" => ("Tikhonov"), "2" => ("Total Variation TV"), "3" => ("Good's Roughness GR")])
# ╔═╡ 5ae1a6a3-4505-4123-9f1e-8a1d4ac0b4e1
reg = [reg_tik, reg_TV, reg_GR][parse(Int, reg_list2)]
# ╔═╡ 15d54e5e-64f4-4a1d-8cc8-9334b2e3784f
md"
iterations =
$(@bind iter Slider(0:50, show_value=true))
λ = $(@bind λ Slider(0:0.001:0.3, show_value=true))
regularizer = $(@bind reg_bool CheckBox())"
# ╔═╡ 803368e6-53fd-4413-b3f5-ffe46ee8983e
img_deconv, res_img = deconvolution(img_blurry, psf, regularizer=reg_bool ? reg : nothing, iterations=iter, λ=λ);
# ╔═╡ e58e1f63-2c81-48fb-866a-4bb70bd428a6
Gray.(img_deconv)
# ╔═╡ 438a6639-bd35-464f-a81d-d98eb65e006e
res_1D, o = deconvolution(real(blur(img_1D)), psf_1D, iterations=iter, regularizer=reg_1D, λ=0.01);
# ╔═╡ 7a16df73-95ad-47f5-907c-6fd23c6000cf
[Gray.(img) Gray.(img_blurry) Gray.(img_deconv)]
# ╔═╡ 5c8030b7-8805-4771-9329-23abb2744544
begin
plot(freqs, abs.(ffts(img_blurry)[:, 128]), yaxis=:log, ylabel="abs of FFT output in AU", xlabel="frequency in 1/px", ylims=(1e-4, 1e2), label="blurred")
plot!(freqs, abs.(ffts(img)[:, 128]), yaxis=:log,
ylims=(1e-4, 1e4), label="ground truth")
plot!(freqs, abs.(ffts(img_deconv)[:, 128]), label="deconvolved image")
end
# ╔═╡ ff9af79c-f06c-42ac-9c8d-6f09d2ff4056
[Gray.(img_1D); Gray.(res_1D)];
# ╔═╡ d8aee845-e922-41da-a17e-37ffa3e692f0
md"### Real Microscopy Data"
# ╔═╡ fc93fa3d-8599-463b-b9e6-8043b90e9d63
load("figures/real_data_large.png")
# ╔═╡ 97c45bfd-d1ef-49ad-908d-7360c03b0170
md"Image taken from [DeconvolutionLab2](http://bigwww.epfl.ch/deconvolution/deconvolutionlab2/)."
# ╔═╡ bf37664a-f726-46b6-9592-da419165af91
md"## Conclusion - DeconvOptim.jl
"
# ╔═╡ f8117250-bac8-43a1-aae4-5c8bab3a522d
[Gray.(ones(130, 012)) load("../docs/src/assets/logo.png")]
# ╔═╡ b5a70276-e9b9-46e8-8c67-0cad2cfa19da
md"* Flexible Image Deconvolution Software
* N-dimensional signal deconvolution
* Works both on CPU and GPUs
* GPUs usually 5-15x speed improvement
"
# ╔═╡ Cell order:
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