Randomized Singular Value Decomposition Research Articles

A Randomized Singular Value Decomposition Based Linear Programming Technique for Robotic Radiation Therapy Treatment Plan Optimization

With highly reliable control of linac positioning, the robotic radiotherapy by CyberKnife significantly increases the freedom in radiation beam placement, but also imposes more challenges on treatment plan optimization. The resampling mechanism in vendor supplied treatment planning system (MultiPlan) could not fully explore the increased beam direction search space. This study proposes a randomized singular value decomposition (RSVD) based linear programming (LP) technique for circular collimator robotic radiotherapy treatment plan optimization (CCRTPO). The RSVDLP algorithm initializes beam angle of each available node is to cover the entire target with equivalent beam taper, which fully explores the complete beam space without redundancy. Beam weight is optimized by LP, which minimizes the deviation of relax constraints (RCs) subjected to hard constraints. Based on the degeneracy of dose influence matrix (DIM), of which the column vector is the dose delivered by one beam to all voxels, a RSVD approach is developed to compress the weight variables, and back project the compressed variables to construct beam weights after optimization. The beams with lower weight are removed, and the weight of remaining beams is further optimized using the same method to reduce number of beams. The technique was demonstrated and compared with the MultiPlan on a lung case with a PTV of 15.5cm3. Both algorithms used the same set of 94 nodes, and circular collimators of 15mm & 20mm diameter. The objectives and constraints used in MultiPlan are switched in RSVDLP model. The switched model is more suitable for SBRT, as it guarantees sufficient dose for PTV and avoids cold spot. For spinal cord (SC) and trachea (Tr), RSVDLP model uses stricter RCs to achieve better protection without triggering infeasibility. RSVD is performed to preserve 90% feature of DIM, the compression rate is 24.4% (1670 compressed variables over 6832 initial beams), and the optimization is sped up 4.8 times (1785s over 370s). The table indicates that RSVDLP plan achieves better homogeneity, conformity and OAR protection with lower MU and fewer beams. Similar results were observed on liver and brain cases.Abstract 3639; Table Comparison of optimization models and results (unit in cGy)Objective (O) & constraint (C)DmaxDmeanCI2HIMUBeam #PTVSCEsTrSCEsTrLLRLRSVDLP>4500 C<4650 O<1200 O<2200 O<1200 O1613304913561173491.281.1735745134MultiPlan>4500 O<4650 C<1500 C<4150 C<4050 O<2200 C1681318016591453621.581.2837820136Abbr: esophagus-Es, left lung-LL, right lung-RL, conformity index-CI, homogeneity index-HI. Open table in a new tab Abbr: esophagus-Es, left lung-LL, right lung-RL, conformity index-CI, homogeneity index-HI. We have developed a RSVDLP technique for CCRTPO. The results demonstrate that RSVD is effective in accelerating the optimization. Due to the use of complete beam space and flexible model, the plan generated by RSVDLP achieves better dose distribution than MultiPlan.

Preconditioned prestack plane-wave least squares reverse time migration with singular spectrum constraint

Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration (PLSRTM) method with singular spectrum constraint. Singular spectrum analysis (SSA) is used in the preconditioning of the take-offangle-domain common-image gathers (TADCIGs). In addition, we adopt randomized singular value decomposition (RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition (SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.

Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation

Due to the low-dimensional property of clean hyperspectral images (HSIs), many low-rank-based methods have been proposed to denoise HSIs. However, in an HSI, the noise intensity in different bands is often different, and most of the existing methods do not take this fact into consideration. In this paper, a noise-adjusted iterative low-rank matrix approximation (NAILRMA) method is proposed for HSI denoising. Based on the low-rank property of HSIs, the patchwise low-rank matrix approximation (LRMA) is established. To further separate the noise from the signal subspaces, an iterative regularization framework is proposed. Considering that the noise intensity in different bands is different, an adaptive iteration factor selection based on the noise variance of each HSI band is adopted. This noise-adjusted iteration strategy can effectively preserve the high-SNR bands and denoise the low-SNR bands. The randomized singular value decomposition (RSVD) method is then utilized to solve the NAILRMA optimization problem. A number of experiments were conducted in both simulated and real data conditions to illustrate the performance of the proposed NAILRMA method for HSI denoising.

RSVD-based Dimensionality Reduction for RecommenderSystems

We investigate dimensionality reduction methods from the perspective of their ability to produce a low-rank customer-product matrix representation. We analyze the results of using collaborative filtering based on SVD, RI, Reflective Random Indexing (RRI) and Randomized Singular Value Decomposition (RSVD) from the perspective of selected algebraic (i.e. application-independent) properties. We show that the Frobenius-norm optimality of SVD does not correspond to the optimal recommendation accuracy, when measured in terms of F1. On the other hand, a high collaborative filtering quality is achievable when a matrix decomposition - based on a combination of RRI and SVD referred to as RSVD-RRI - leads to increased diversity of low-dimensional eigenvectors. The diversity is observable from the perspective of cosine similarities analyzed in comparison to the analogical case of SVD. Such a feature is more desirable than the fidelity of the input matrix spectrum representation, despite the MSE-optimality of SVD.