Mercurial > repos > PredictPDPS / file comparison
comparison: src/PET/AlgorithmZeroDual.jl
src/PET/AlgorithmZeroDual.jl
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| 1 #################################################################### | |
| 2 # Predictive online PDPS for optical flow with known velocity field | |
| 3 #################################################################### | |
| 4 | |
| 5 __precompile__() | |
| 6 | |
| 7 module AlgorithmZeroDual | |
| 8 | |
| 9 identifier = "pdps_known_zerodual" | |
| 10 | |
| 11 using Printf | |
| 12 | |
| 13 using AlgTools.Util | |
| 14 import AlgTools.Iterate | |
| 15 using ImageTools.Gradient | |
| 16 using ImageTools.Translate | |
| 17 | |
| 18 using ..Radon | |
| 19 using ImageTransformations | |
| 20 using Images, CoordinateTransformations, Rotations, OffsetArrays | |
| 21 using ImageCore, Interpolations | |
| 22 | |
| 23 using ..OpticalFlow: ImageSize, | |
| 24 Image, | |
| 25 petpdflow! | |
| 26 | |
| 27 ######################### | |
| 28 # Iterate initialisation | |
| 29 ######################### | |
| 30 | |
| 31 function init_rest(x::Image) | |
| 32 imdim=size(x) | |
| 33 y = zeros(2, imdim...) | |
| 34 Δx = copy(x) | |
| 35 Δy = copy(y) | |
| 36 x̄ = copy(x) | |
| 37 radonx = copy(x) | |
| 38 return x, y, Δx, Δy, x̄, radonx | |
| 39 end | |
| 40 | |
| 41 function init_iterates(xinit::Image) | |
| 42 return init_rest(copy(xinit)) | |
| 43 end | |
| 44 | |
| 45 function init_iterates(dim::ImageSize) | |
| 46 return init_rest(zeros(dim...)) | |
| 47 end | |
| 48 | |
| 49 ######################### | |
| 50 # PETscan related | |
| 51 ######################### | |
| 52 function petvalue(x, b, c) | |
| 53 tmp = similar(b) | |
| 54 radon!(tmp, x) | |
| 55 return sum(@. tmp - b*log(tmp+c)) | |
| 56 end | |
| 57 | |
| 58 function petgrad!(res, x, b, c, S) | |
| 59 tmp = similar(b) | |
| 60 radon!(tmp, x) | |
| 61 @. tmp = S .- b/(tmp+c) | |
| 62 backproject!(res, S.*tmp) | |
| 63 end | |
| 64 | |
| 65 function proj_nonneg!(y) | |
| 66 @inbounds @simd for i=1:length(y) | |
| 67 if y[i] < 0 | |
| 68 y[i] = 0 | |
| 69 end | |
| 70 end | |
| 71 return y | |
| 72 end | |
| 73 | |
| 74 ############ | |
| 75 # Algorithm | |
| 76 ############ | |
| 77 | |
| 78 function solve( :: Type{DisplacementT}; | |
| 79 dim :: ImageSize, | |
| 80 iterate = AlgTools.simple_iterate, | |
| 81 params::NamedTuple) where DisplacementT | |
| 82 | |
| 83 ################################ | |
| 84 # Extract and set up parameters | |
| 85 ################################ | |
| 86 α, ρ = params.α, params.ρ | |
| 87 R_K² = ∇₂_norm₂₂_est² | |
| 88 γ = 1 | |
| 89 L = params.L | |
| 90 τ₀, σ₀ = params.τ₀, params.σ₀ | |
| 91 τ = τ₀/L | |
| 92 σ = σ₀*(1-τ₀)/(R_K²*τ) | |
| 93 | |
| 94 println("Step length parameters: τ=$(τ), σ=$(σ)") | |
| 95 | |
| 96 λ = params.λ | |
| 97 c = params.c*ones(params.radondims...) | |
| 98 | |
| 99 | |
| 100 ###################### | |
| 101 # Initialise iterates | |
| 102 ###################### | |
| 103 | |
| 104 x, y, Δx, Δy, x̄, r∇ = init_iterates(dim) | |
| 105 | |
| 106 if params.L_experiment | |
| 107 oldpetgradx = zeros(size(x)...) | |
| 108 petgradx = zeros(size(x)) | |
| 109 oldx = ones(size(x)) | |
| 110 end | |
| 111 | |
| 112 #################### | |
| 113 # Run the algorithm | |
| 114 #################### | |
| 115 | |
| 116 v = iterate(params) do verbose :: Function, | |
| 117 b :: Image, # noisy_sinogram | |
| 118 v_known :: DisplacementT, | |
| 119 theta_known :: DisplacementT, | |
| 120 b_true :: Image, | |
| 121 S :: Image | |
| 122 | |
| 123 ################### | |
| 124 # Prediction steps | |
| 125 ################### | |
| 126 | |
| 127 petpdflow!(x, Δx, y, Δy, v_known, theta_known, false) | |
| 128 y .= zeros(size(y)...) | |
| 129 | |
| 130 if params.L_experiment | |
| 131 @. oldx = x | |
| 132 end | |
| 133 | |
| 134 ############ | |
| 135 # PDPS step | |
| 136 ############ | |
| 137 | |
| 138 ∇₂ᵀ!(Δx, y) # primal step: | |
| 139 @. x̄ = x # | save old x for over-relax | |
| 140 petgrad!(r∇, x, b, c, S) # | Calculate gradient of fidelity term | |
| 141 | |
| 142 @. x = x-(τ*λ)*r∇-τ*Δx # | | |
| 143 proj_nonneg!(x) # | non-negativity constaint prox | |
| 144 @. x̄ = 2x - x̄ # over-relax: x̄ = 2x-x_old | |
| 145 ∇₂!(Δy, x̄) # dual step: | |
| 146 @. y = y + σ*Δy # | | |
| 147 proj_norm₂₁ball!(y, α) # | prox | |
| 148 | |
| 149 ##################### | |
| 150 # L update if needed | |
| 151 ##################### | |
| 152 if params.L_experiment | |
| 153 petgrad!(petgradx, x, b, c, S) | |
| 154 petgrad!(oldpetgradx, oldx, b, c, S) | |
| 155 if norm₂(x-oldx)>1e-12 | |
| 156 L = max(0.9*norm₂(petgradx - oldpetgradx)/norm₂(x-oldx),L) | |
| 157 println("Step length parameters: L=$(L)") | |
| 158 τ = τ₀/L | |
| 159 σ = σ₀*(1-τ₀)/(R_K²*τ) | |
| 160 end | |
| 161 end | |
| 162 | |
| 163 ################################ | |
| 164 # Give function value if needed | |
| 165 ################################ | |
| 166 | |
| 167 v = verbose() do | |
| 168 ∇₂!(Δy, x) | |
| 169 value = λ*petvalue(x, b, c) + params.α*norm₂₁(Δy) | |
| 170 value, x, [NaN, NaN], nothing, τ, σ | |
| 171 end | |
| 172 | |
| 173 v | |
| 174 end | |
| 175 | |
| 176 return x, y, v | |
| 177 end | |
| 178 | |
| 179 end # Module | |
| 180 | |
| 181 |
