From 9aa30ad59e54d7b5c2d8b61d795c0dbf42329f8b Mon Sep 17 00:00:00 2001
From: roflmaostc <fxw+git@mailbox.org>
Date: Tue, 28 May 2024 11:29:31 +0200
Subject: [PATCH 1/3] Add GPU example

---
 notebooks/convolution_GPU_example.jl | 1506 ++++++++++++++++++++++++++
 1 file changed, 1506 insertions(+)
 create mode 100644 notebooks/convolution_GPU_example.jl

diff --git a/notebooks/convolution_GPU_example.jl b/notebooks/convolution_GPU_example.jl
new file mode 100644
index 0000000..db927d5
--- /dev/null
+++ b/notebooks/convolution_GPU_example.jl
@@ -0,0 +1,1506 @@
+### A Pluto.jl notebook ###
+# v0.19.41
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 02814ffd-991c-4672-8791-168564e5a869
+using CUDA, TestImages, IndexFunArrays, PlutoUI, ImageShow, FFTW
+
+# ╔═╡ a2714150-f737-4ddc-a2b7-c9ada01a58e7
+using DifferentiationInterface, Optim, Optim
+
+# ╔═╡ 23d7995b-7cbd-4e42-97da-1e503db13920
+import Enzyme, Zygote, ReverseDiff
+
+# ╔═╡ 2615f780-089a-41d6-a043-505a21d441f7
+TableOfContents()
+
+# ╔═╡ 7d6ed1ef-3271-4cbd-8f5e-e13a7b22a4e1
+ImageShow.simshow(x::CuArray; kwargs...) = simshow(Array(x); kwargs...)
+
+# ╔═╡ 8f05639c-310e-4d53-b342-f2da13a971cc
+use_CUDA = Ref(true)
+
+# ╔═╡ 4aff1c79-e214-494e-a1d3-5a52224baeba
+md" ## CUDA
+CUDA accelerates operations on large arrays easily by 5-20 times!
+
+Your CUDA is functional: **$(use_CUDA[])**
+"
+
+# ╔═╡ dfe77e52-81ef-4019-866a-070a713a65cf
+var"@mytime" = use_CUDA[] ? CUDA.var"@time" : var"@time"
+
+# ╔═╡ 0ce337ba-6c40-4008-9cb6-79e3533f72d7
+togoc(x) = use_CUDA[] ? CuArray(x) : x
+
+# ╔═╡ b01b8419-45d4-42f2-aee8-99316ccfd9ab
+md"# Background
+
+In this example we want to demonstrate an inverse optimization problem.
+Given an blurry measurement $Y$ we seek to recover the image $X$ which has been convolved with $h$:
+
+$$Y = X * h$$
+
+To solve this equation, we can write this as a general inverse problem, where we want to find a minimum for the loss function $\mathcal{L}$:
+
+$$\mathcal{L} = \sum_i |Y_i - (\hat X * h)_i|$$
+
+We then use gradient descent and automatic differentiation to find a solution to this deconvolution problem.
+"
+
+# ╔═╡ 453eae77-2781-49d8-81db-da3b47bb0a59
+md"# Load an image and create blurring kernel h"
+
+# ╔═╡ 03291d99-3c4d-4280-b3ff-4b273475efc1
+X = togoc(Float32.(testimage("resolution_test_512")));
+
+# ╔═╡ 780a71fb-be1f-44f5-992c-ef788ee24cf0
+h = togoc(normal(Float32, size(X), sigma=3));
+
+# ╔═╡ 0aac6cb2-92e5-4514-ae2c-49404e4fbef9
+md"# Create a forward model"
+
+# ╔═╡ 334de576-c89c-4fda-8a1d-a7fb0ef87fd6
+"""
+	conv(x, h)
+
+Implement a FFT based convolution operation
+"""
+function conv(x, h)
+	return real(ifft(fft(x) .* fft(ifftshift(h))))
+end;
+
+# ╔═╡ 9794931f-1bcf-45e8-a5b4-7b251d55986a
+md"# Create measurement"
+
+# ╔═╡ 8e8a3e4c-63f8-4898-885a-ba87ef207a1f
+Y = conv(X, h) .+ togoc(0.01f0 .* randn(Float32, size(X)));
+
+# ╔═╡ d1ab09a8-2baf-471e-8185-337ac5bd693c
+[simshow(X) simshow(ones((512, 10))) simshow(h) simshow(ones((512, 10))) simshow(Y) ]
+
+# ╔═╡ 409965c7-65dd-419b-83d6-ec3d2d6f52f2
+md"# Define loss function and gradient"
+
+# ╔═╡ 88cb7289-e76d-4a99-bd16-dbb48cc3023e
+loss(x) = sum(abs2, Y .- conv(x, h))
+
+# ╔═╡ 40819db4-0b56-4a4c-993e-309d19eb0dae
+gradient!(G, x) = DifferentiationInterface.gradient!(loss, G, AutoZygote(), x)
+
+# ╔═╡ f3a9bbc3-ad1b-47f4-9a9f-5ef4ca83d602
+md"# Do the optimization"
+
+# ╔═╡ 8497d788-21cf-40de-9b24-71ff0cdfc1ed
+initial_guess = togoc(zeros(Float32, size(X)));
+
+# ╔═╡ ef2206bf-3e18-4152-80c2-455228785d2f
+@mytime res = Optim.optimize(loss, gradient!, initial_guess, LBFGS(), Optim.Options(iterations=30))
+
+# ╔═╡ 9c95e2f6-4201-4754-a363-510203d6e3bb
+[simshow(X) simshow(ones((512, 10))) simshow(Y) simshow(ones((512, 10))) simshow(res.minimizer) ]
+
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+
+    [deps.StructArrays.extensions]
+    StructArraysAdaptExt = "Adapt"
+    StructArraysGPUArraysCoreExt = "GPUArraysCore"
+    StructArraysSparseArraysExt = "SparseArrays"
+    StructArraysStaticArraysExt = "StaticArrays"
+
+[[deps.StructIO]]
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+
+[[deps.SuiteSparse_jll]]
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+
+[[deps.TOML]]
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+
+[[deps.TableTraits]]
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+[[deps.Tables]]
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+[[deps.Test]]
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+[[deps.TestImages]]
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+[[deps.TiffImages]]
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+[[deps.TimerOutputs]]
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+[[deps.Tricks]]
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+[[deps.URIs]]
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+[[deps.UUIDs]]
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+[[deps.UnPack]]
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+[[deps.XZ_jll]]
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+
+[[deps.Zlib_jll]]
+deps = ["Libdl"]
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+
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.6+0"
+
+[[deps.Zygote]]
+deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "GPUArrays", "GPUArraysCore", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "PrecompileTools", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "19c586905e78a26f7e4e97f81716057bd6b1bc54"
+uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
+version = "0.6.70"
+
+    [deps.Zygote.extensions]
+    ZygoteColorsExt = "Colors"
+    ZygoteDistancesExt = "Distances"
+    ZygoteTrackerExt = "Tracker"
+
+    [deps.Zygote.weakdeps]
+    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
+    Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
+[[deps.ZygoteRules]]
+deps = ["ChainRulesCore", "MacroTools"]
+git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.5"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.8.0+1"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.43+1"
+
+[[deps.libsixel_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
+git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
+uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
+version = "1.10.3+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.52.0+1"
+
+[[deps.oneTBB_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
+uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
+version = "2021.12.0+0"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+version = "17.4.0+2"
+"""
+
+# ╔═╡ Cell order:
+# ╠═02814ffd-991c-4672-8791-168564e5a869
+# ╠═a2714150-f737-4ddc-a2b7-c9ada01a58e7
+# ╠═23d7995b-7cbd-4e42-97da-1e503db13920
+# ╠═2615f780-089a-41d6-a043-505a21d441f7
+# ╟─4aff1c79-e214-494e-a1d3-5a52224baeba
+# ╠═7d6ed1ef-3271-4cbd-8f5e-e13a7b22a4e1
+# ╠═8f05639c-310e-4d53-b342-f2da13a971cc
+# ╠═dfe77e52-81ef-4019-866a-070a713a65cf
+# ╠═0ce337ba-6c40-4008-9cb6-79e3533f72d7
+# ╟─b01b8419-45d4-42f2-aee8-99316ccfd9ab
+# ╟─453eae77-2781-49d8-81db-da3b47bb0a59
+# ╠═03291d99-3c4d-4280-b3ff-4b273475efc1
+# ╠═780a71fb-be1f-44f5-992c-ef788ee24cf0
+# ╟─0aac6cb2-92e5-4514-ae2c-49404e4fbef9
+# ╟─334de576-c89c-4fda-8a1d-a7fb0ef87fd6
+# ╠═d1ab09a8-2baf-471e-8185-337ac5bd693c
+# ╟─9794931f-1bcf-45e8-a5b4-7b251d55986a
+# ╠═8e8a3e4c-63f8-4898-885a-ba87ef207a1f
+# ╟─409965c7-65dd-419b-83d6-ec3d2d6f52f2
+# ╠═88cb7289-e76d-4a99-bd16-dbb48cc3023e
+# ╠═40819db4-0b56-4a4c-993e-309d19eb0dae
+# ╟─f3a9bbc3-ad1b-47f4-9a9f-5ef4ca83d602
+# ╠═8497d788-21cf-40de-9b24-71ff0cdfc1ed
+# ╠═ef2206bf-3e18-4152-80c2-455228785d2f
+# ╠═9c95e2f6-4201-4754-a363-510203d6e3bb
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002

From 4209a48a26665a1bb3db946ac65f927bbf7e0109 Mon Sep 17 00:00:00 2001
From: roflmaostc <fxw+git@mailbox.org>
Date: Tue, 28 May 2024 11:42:11 +0200
Subject: [PATCH 2/3] Add regularizer

---
 notebooks/convolution_GPU_example.jl | 41 ++++++++++++++++++++++++++--
 1 file changed, 38 insertions(+), 3 deletions(-)

diff --git a/notebooks/convolution_GPU_example.jl b/notebooks/convolution_GPU_example.jl
index db927d5..849de5a 100644
--- a/notebooks/convolution_GPU_example.jl
+++ b/notebooks/convolution_GPU_example.jl
@@ -45,7 +45,7 @@ $$Y = X * h$$
 
 To solve this equation, we can write this as a general inverse problem, where we want to find a minimum for the loss function $\mathcal{L}$:
 
-$$\mathcal{L} = \sum_i |Y_i - (\hat X * h)_i|$$
+$$\mathcal{L} = \sum_i |Y_i - (\hat X * h)_i|^2$$
 
 We then use gradient descent and automatic differentiation to find a solution to this deconvolution problem.
 "
@@ -76,7 +76,7 @@ end;
 md"# Create measurement"
 
 # ╔═╡ 8e8a3e4c-63f8-4898-885a-ba87ef207a1f
-Y = conv(X, h) .+ togoc(0.01f0 .* randn(Float32, size(X)));
+Y = conv(X, h) .+ togoc(0.1f0 .* randn(Float32, size(X)));
 
 # ╔═╡ d1ab09a8-2baf-471e-8185-337ac5bd693c
 [simshow(X) simshow(ones((512, 10))) simshow(h) simshow(ones((512, 10))) simshow(Y) ]
@@ -97,11 +97,40 @@ md"# Do the optimization"
 initial_guess = togoc(zeros(Float32, size(X)));
 
 # ╔═╡ ef2206bf-3e18-4152-80c2-455228785d2f
-@mytime res = Optim.optimize(loss, gradient!, initial_guess, LBFGS(), Optim.Options(iterations=30))
+@mytime res = Optim.optimize(loss, gradient!, initial_guess, LBFGS(), Optim.Options(iterations=5))
 
 # ╔═╡ 9c95e2f6-4201-4754-a363-510203d6e3bb
 [simshow(X) simshow(ones((512, 10))) simshow(Y) simshow(ones((512, 10))) simshow(res.minimizer) ]
 
+# ╔═╡ 8305c596-c3e7-445c-8465-81deb8c8d661
+md"# Add regularizer
+
+As we have seen, optimizing too many iterations, noise will be amplified.
+To avoid this, we can add a regularizing term to the optimization:
+
+
+$$f_{i,j} = (\hat X * h)_{i,j}$$
+
+$$\mathcal{L} = \sum_{i,j} |Y_{i,j} - f_{i,j}|^2 + \lambda \sqrt{\varepsilon + |f_{i,j}-f_{i,j+1}|^2 + |f_{i+1,j}-f_{i,j}|^2}$$
+
+where $\varepsilon$ is a small value to make this term differentiable. $\lambda$ is the weight factor of the regularizer.
+"
+
+# ╔═╡ 9136ca18-c72d-4afd-ba7d-770f28c6a612
+reg(x) = sum(sqrt.(1f-20 .+ (x .- circshift(x, (1,0))).^2 .+  (x .- circshift(x, (0,1))).^2))
+
+# ╔═╡ 113007e5-c7e3-4267-8b64-faa72aab0ed7
+loss_with_reg(x) = loss(x) + 1f-2 * reg(x)
+
+# ╔═╡ 45a3021f-6d72-418f-a076-e51ab798380e
+gradient_with_reg!(G, x) = DifferentiationInterface.gradient!(loss_with_reg, G, AutoZygote(), x)
+
+# ╔═╡ c62d11b2-7a07-4598-ac76-ab6e07b687bc
+@mytime res_reg = Optim.optimize(loss_with_reg, gradient_with_reg!, initial_guess, LBFGS(), Optim.Options(iterations=30))
+
+# ╔═╡ dc194c82-483e-49c8-97c5-8eb9f14c0784
+[simshow(res.minimizer) simshow(ones((512, 10))) simshow(res_reg.minimizer)]
+
 # ╔═╡ 00000000-0000-0000-0000-000000000001
 PLUTO_PROJECT_TOML_CONTENTS = """
 [deps]
@@ -1502,5 +1531,11 @@ version = "17.4.0+2"
 # ╠═8497d788-21cf-40de-9b24-71ff0cdfc1ed
 # ╠═ef2206bf-3e18-4152-80c2-455228785d2f
 # ╠═9c95e2f6-4201-4754-a363-510203d6e3bb
+# ╟─8305c596-c3e7-445c-8465-81deb8c8d661
+# ╠═9136ca18-c72d-4afd-ba7d-770f28c6a612
+# ╠═113007e5-c7e3-4267-8b64-faa72aab0ed7
+# ╠═45a3021f-6d72-418f-a076-e51ab798380e
+# ╠═c62d11b2-7a07-4598-ac76-ab6e07b687bc
+# ╠═dc194c82-483e-49c8-97c5-8eb9f14c0784
 # ╟─00000000-0000-0000-0000-000000000001
 # ╟─00000000-0000-0000-0000-000000000002

From 92d228eae006e872017df7af6740c6815a569f79 Mon Sep 17 00:00:00 2001
From: roflmaostc <fxw+git@mailbox.org>
Date: Tue, 28 May 2024 11:54:00 +0200
Subject: [PATCH 3/3] Add convolution code

---
 notebooks/convolution_GPU_example.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/notebooks/convolution_GPU_example.jl b/notebooks/convolution_GPU_example.jl
index 849de5a..7ae18d3 100644
--- a/notebooks/convolution_GPU_example.jl
+++ b/notebooks/convolution_GPU_example.jl
@@ -26,7 +26,7 @@ use_CUDA = Ref(true)
 md" ## CUDA
 CUDA accelerates operations on large arrays easily by 5-20 times!
 
-Your CUDA is functional: **$(use_CUDA[])**
+**$(use_CUDA[] ? \" Your CUDA is functional\" : \" Your CUDA is not functional  \")**
 "
 
 # ╔═╡ dfe77e52-81ef-4019-866a-070a713a65cf
@@ -97,7 +97,7 @@ md"# Do the optimization"
 initial_guess = togoc(zeros(Float32, size(X)));
 
 # ╔═╡ ef2206bf-3e18-4152-80c2-455228785d2f
-@mytime res = Optim.optimize(loss, gradient!, initial_guess, LBFGS(), Optim.Options(iterations=5))
+@mytime res = Optim.optimize(loss, gradient!, initial_guess, LBFGS(), Optim.Options(iterations=20))
 
 # ╔═╡ 9c95e2f6-4201-4754-a363-510203d6e3bb
 [simshow(X) simshow(ones((512, 10))) simshow(Y) simshow(ones((512, 10))) simshow(res.minimizer) ]