src/PET/AlgorithmRotation.jl

Fri, 19 Apr 2024 17:05:54 +0300

author
Neil Dizon <neil.dizon@helsinki.fi>
date
Fri, 19 Apr 2024 17:05:54 +0300
changeset 9
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parent 8
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child 13
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permissions
-rw-r--r--

readme corrections

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

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