Kronecker Product Approximation for Three-Dimensional Imaging Applications
نویسندگان
چکیده
Kronecker product and tensor decompositions are used to construct approximations of severely ill-conditioned matrices that arise in three-dimensional image processing applications. Computa-tionally efficient methods to construct the approximations are developed by exploiting structure that is inherent in many image processing problems, such as those arising in microscopy and medical imaging. It is shown that the resulting approximations provide a general, powerful tool that can be used to improve efficiency of image reconstruction algorithms.
منابع مشابه
Best Kronecker Product Approximation of The Blurring Operator in Three Dimensional Image Restoration Problems
In this paper, we propose a method to find the best Kronecker product approximation of the blurring operator which arises in three dimensional image restoration problems. We show that this problem can be reduced to a well known rank-1 approximation of the scaled three dimensional point spread function (PSF) array, which is much smaller. This approximation can be used as a preconditioner in solv...
متن کاملKronecker Product Approximations forImage Restoration with Reflexive Boundary Conditions
Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. Wh...
متن کاملSketching for Kronecker Product Regression and P-splines
TensorSketch is an oblivious linear sketch introduced in (Pagh, 2013) and later used in (Pham and Pagh, 2013) in the context of SVMs for polynomial kernels. It was shown in (Avron et al., 2014) that TensorSketch provides a subspace embedding, and therefore can be used for canonical correlation analysis, low rank approximation, and principal component regression for the polynomial kernel. We tak...
متن کاملKronecker product approximation preconditioners for convection-diffusion model problems
We consider the iterative solution of linear systems arising from four convection–diffusion model problems: scalar convection–diffusion problem, Stokes problem, Oseen problem and Navier–Stokes problem. We design preconditioners for these model problems that are based on Kronecker product approximations (KPAs). For this we first identify explicit Kronecker product structure of the coefficient ma...
متن کاملFast Subspace Clustering Based on the Kronecker Product
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace gener...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004