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readme corrections
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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 |