Optimization Degrees Of Freedom Research Articles

Minimum-monitor-unit optimization via a stochastic coordinate descent method

Objective. Deliverable proton spots are subject to the minimum monitor-unit (MMU) constraint. The MMU optimization problem with relatively large MMU threshold remains mathematically challenging due to its strong nonconvexity. However, the MMU optimization is fundamental to proton radiotherapy (RT), including efficient IMPT and proton arc delivery (ARC). This work aims to develop a new optimization algorithm that is effective in solving the MMU problem. Approach. Our new algorithm is primarily based on stochastic coordinate decent (SCD) method. It involves three major steps: first to decouple the determination of active sets for dose-volume-histogram (DVH) planning constraints from the MMU problem via iterative convex relaxation method; second to handle the nonconvexity of the MMU constraint via SCD to localize the index set of nonzero spots; third to solve convex subproblems projected to this convex set of nonzero spots via projected gradient descent method. Main results. Our new method SCD is validated and compared with alternating direction method of multipliers (ADMM) for IMPT and ARC. The results suggest SCD had better plan quality than ADMM, e.g. the improvement of conformal index (CI) from 0.56 to 0.69 during IMPT, and from 0.28 to 0.80 during ARC for the lung case. Moreover, SCD successfully handled the nonconvexity from large MMU threshold that ADMM failed to handle, in the sense that (1) the plan quality from ARC was worse than IMPT (e.g. CI was 0.28 with IMPT and 0.56 with ARC for the lung case), when ADMM was used; (2) in contrast, with SCD, ARC achieved better plan quality than IMPT (e.g. CI was 0.69 with IMPT and 0.80 with ARC for the lung case), which is compatible with more optimization degrees of freedom from ARC compared to IMPT. Significance. To the best of our knowledge, our new MMU optimization method via SCD can effectively handle the nonconvexity from large MMU threshold that none of the current methods can solve. Therefore, we have developed a unique MMU optimization algorithm via SCD that can be used for efficient IMPT, proton ARC, and other particle RT applications where large MMU threshold is desirable (e.g. for the delivery of high dose rates or/and a large number of spots).

Constructal Design of an Arrow-Shaped High Thermal Conductivity Channel in a Square Heat Generation Body.

A heat conduction model with an arrow-shaped high thermal conductivity channel (ASHTCC) in a square heat generation body (SHGB) is established in this paper. By taking the minimum maximum temperature difference (MMTD) as the optimization goal, constructal designs of the ASHTCC are conducted based on single, two, and three degrees of freedom optimizations under the condition of fixed ASHTCC material. The outcomes illustrate that the heat conduction performance (HCP) of the SHGB is better when the structure of the ASHTCC tends to be flat. Increasing the thermal conductivity ratio and area fraction of the ASHTCC material can improve the HCP of the SHGB. In the discussed numerical examples, the MMTD obtained by three degrees of freedom optimization are reduced by 8.42% and 4.40%, respectively, compared with those obtained by single and two degrees of freedom optimizations. Therefore, three degrees of freedom optimization can further improve the HCP of the SHGB. Compared the HCPs of the SHGBs with ASHTCC and the T-shaped one, the MMTD of the former is reduced by 13.0%. Thus, the structure of the ASHTCC is proven to be superior to that of the T-shaped one. The optimization results gained in this paper have reference values for the optimal structure designs for the heat dissipations of various electronic devices.

Full-field Fourier ptychography (FFP): Spatially varying pupil modeling and its application for rapid field-dependent aberration metrology

Digital aberration measurement and removal play a prominent role in computational imaging platforms aimed at achieving simple and compact optical arrangements. A recent important class of such platforms is Fourier ptychography (FP), which is geared toward efficiently creating gigapixel images with high resolution and large field of view (FOV). In current FP implementations, pupil aberration is often recovered at each small segment of the entire FOV. This reconstruction strategy fails to consider the field-dependent nature of the optical pupil. Given the power series expansion of the wavefront aberration, the spatially varying pupil can be fully characterized by tens of coefficients over the entire FOV. With this observation, we report a Full-field Fourier Ptychography (FFP) scheme for rapid and robust aberration metrology. The meaning of “full-field” in FFP is referred to the recovery of the “full-field” coefficients that govern the field-dependent pupil over the entire FOV. The optimization degrees of freedom are at least two orders of magnitude lower than the previous implementations. We show that the image acquisition process of FFP can be completed in ∼1 s and the spatially varying aberration of the entire FOV can be recovered in ∼35 s using a central processing unit. The reported approach may facilitate the further development of FP. Since no moving part or calibration target is needed in this approach, it may find important applications in aberration metrology. The derivation of the full-field coefficients and its extension for Zernike modes also provide a general tool for analyzing spatially varying aberrations in computational imaging systems.