Mercurial > repos > PredictPDPS / file comparison
comparison: src/AlgorithmProximal.jl
src/AlgorithmProximal.jl
- changeset 5
- 843e7611b068
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| 4:a64766c44642 | 5:843e7611b068 |
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| 1 #################################################################### | |
| 2 # Predictive online PDPS for optical flow with known velocity field | |
| 3 #################################################################### | |
| 4 | |
| 5 __precompile__() | |
| 6 | |
| 7 module AlgorithmProximal | |
| 8 | |
| 9 identifier = "pdps_known_proximal" | |
| 10 | |
| 11 using Printf | |
| 12 | |
| 13 using AlgTools.Util | |
| 14 import AlgTools.Iterate | |
| 15 using ImageTools.Gradient | |
| 16 | |
| 17 using ..OpticalFlow: ImageSize, | |
| 18 Image, | |
| 19 pdflow! | |
| 20 | |
| 21 ######################### | |
| 22 # Iterate initialisation | |
| 23 ######################### | |
| 24 | |
| 25 function init_rest(x::Image) | |
| 26 imdim=size(x) | |
| 27 | |
| 28 y = zeros(2, imdim...) | |
| 29 Δx = copy(x) | |
| 30 Δy = copy(y) | |
| 31 x̄ = copy(x) | |
| 32 | |
| 33 return x, y, Δx, Δy, x̄ | |
| 34 end | |
| 35 | |
| 36 function init_iterates(xinit::Image) | |
| 37 return init_rest(copy(xinit)) | |
| 38 end | |
| 39 | |
| 40 function init_iterates(dim::ImageSize) | |
| 41 return init_rest(zeros(dim...)) | |
| 42 end | |
| 43 | |
| 44 ############ | |
| 45 # Algorithm | |
| 46 ############ | |
| 47 | |
| 48 function step_lengths(params, γ, R_K²) | |
| 49 ρ̃₀, τ₀, σ₀, σ̃₀ = params.ρ̃₀, params.τ₀, params.σ₀, params.σ̃₀ | |
| 50 δ = params.δ | |
| 51 ρ = isdefined(params, :phantom_ρ) ? params.phantom_ρ : params.ρ | |
| 52 Λ = params.Λ | |
| 53 Θ = params.dual_flow ? Λ : 1 | |
| 54 | |
| 55 τ = τ₀/γ | |
| 56 @assert(1+γ*τ ≥ Λ) | |
| 57 σ = σ₀*min(1/(τ*R_K²), 1/max(0, τ*R_K²/((1+γ*τ-Λ)*(1-δ))-ρ)) | |
| 58 q = δ*(1+σ*ρ)/Θ | |
| 59 if 1 ≥ q | |
| 60 σ̃ = σ̃₀*σ/q | |
| 61 #ρ̃ = ρ̃₀*max(0, ((Θ*σ)/(2*δ*σ̃^2*(1+σ*ρ))+1/(2σ)-1/σ̃)) | |
| 62 ρ̃ = max(0, (1-q)/(2*σ)) | |
| 63 else | |
| 64 σ̃ = σ̃₀*σ/(q*(1-√(1-1/q))) | |
| 65 ρ̃ = 0 | |
| 66 end | |
| 67 | |
| 68 println("Step length parameters: τ=$(τ), σ=$(σ), σ̃=$(σ̃), ρ̃=$(ρ̃)") | |
| 69 | |
| 70 return τ, σ, σ̃, ρ̃ | |
| 71 end | |
| 72 | |
| 73 function solve( :: Type{DisplacementT}; | |
| 74 dim :: ImageSize, | |
| 75 iterate = AlgTools.simple_iterate, | |
| 76 params::NamedTuple) where DisplacementT | |
| 77 | |
| 78 ################################ | |
| 79 # Extract and set up parameters | |
| 80 ################################ | |
| 81 | |
| 82 α, ρ = params.α, params.ρ | |
| 83 R_K² = ∇₂_norm₂₂_est² | |
| 84 γ = 1 | |
| 85 τ, σ, σ̃, ρ̃ = step_lengths(params, γ, R_K²) | |
| 86 | |
| 87 ###################### | |
| 88 # Initialise iterates | |
| 89 ###################### | |
| 90 | |
| 91 x, y, Δx, Δy, x̄ = init_iterates(dim) | |
| 92 init_data = (params.init == :data) | |
| 93 | |
| 94 #################### | |
| 95 # Run the algorithm | |
| 96 #################### | |
| 97 | |
| 98 v = iterate(params) do verbose :: Function, | |
| 99 b :: Image, | |
| 100 v_known :: DisplacementT, | |
| 101 🚫unused_b_next :: Image | |
| 102 | |
| 103 ################## | |
| 104 # Prediction step | |
| 105 ################## | |
| 106 if init_data | |
| 107 x .= b | |
| 108 init_data = false | |
| 109 end | |
| 110 | |
| 111 pdflow!(x, Δx, y, Δy, v_known, params.dual_flow) | |
| 112 | |
| 113 # Proximal step | |
| 114 ∇₂!(Δy, x) | |
| 115 @. y = (y + σ̃*Δy)/(1 + σ̃*(ρ̃+ρ/α)) | |
| 116 proj_norm₂₁ball!(y, α) | |
| 117 | |
| 118 | |
| 119 ############ | |
| 120 # PDPS step | |
| 121 ############ | |
| 122 | |
| 123 ∇₂ᵀ!(Δx, y) # primal step: | |
| 124 @. x̄ = x # | save old x for over-relax | |
| 125 @. x = (x-τ*(Δx-b))/(1+τ) # | prox | |
| 126 @. x̄ = 2x - x̄ # over-relax | |
| 127 ∇₂!(Δy, x̄) # dual step: y | |
| 128 @. y = (y + σ*Δy)/(1 + σ*ρ/α) # | | |
| 129 proj_norm₂₁ball!(y, α) # | prox | |
| 130 | |
| 131 ################################ | |
| 132 # Give function value if needed | |
| 133 ################################ | |
| 134 v = verbose() do | |
| 135 ∇₂!(Δy, x) | |
| 136 value = norm₂²(b-x)/2 + params.α*γnorm₂₁(Δy, params.ρ) | |
| 137 value, x, [NaN, NaN], nothing | |
| 138 end | |
| 139 | |
| 140 v | |
| 141 end | |
| 142 | |
| 143 return x, y, v | |
| 144 end | |
| 145 | |
| 146 end # Module | |
| 147 | |
| 148 |
