Radiation doses are optimized by providing a model of the set of beams and a target dose in normalized forms. A Gram matrix is determined from the model. The target dose is subsampled to determine initial intensity values for the set of beams. Then, the following steps are iterated until convergence. A very small positive value, 0 < ε <<1, is added to each intensity value to ensure the intensity value is greater than zero. Each intensity value is multiplied by the Gram matrix to determine a product, which is divided element-wise into the normalized target dose to determine corresponding ratios. If the ratios are all close to 1, within a numerical error tolerance,the intensity values of the set of beam are output. Otherwise, the intensity values are multiplied by the ratios before a next iteration.藉由提供一組射束的模型和目標劑量正規化方式對放射劑量進行最佳化。該模型決定格拉姆矩陣(Gram matrix)。該目標劑量為子取樣(subsample),以確定該組射束之初始強度值。然後,重複以下的步驟直至收斂。一非常小的正數(0<ε<<1)加到每一強度值,以確保該強度值大於零。每一強度值乘以格拉姆矩陣以確定乘積,元素智能(element-wise)除以正規化目標劑量以確定相應的比例。如果所有比例都接近1,在數值誤差容限內,輸出該組射束之強度值。否則,於下一次迭代前,該強度值乘以該比例。101...射束模型102...目標劑量103...處於風險之器官110...將射束模型,目標為(選擇性加權)置入正規化形式115...決定120...子取樣目標以獲得初始射束值130...該值加ε乘以射束模型之格拉姆矩陣135...格拉姆矩陣140...結果除以目標之正規化形式150...絕對值(結果-1)<容限?160...輸出射束值170...射束值乘以結果
