Analysis and exploitation of matrix structure arising in linearized optical tomographic imaging

作者：Hyde Damon^*; Kilmer Misha; Brooks Dana H; Miller Eric

来源：SIAM Journal on Matrix Analysis and Applications, 2007, 29(4): 1065-1082.

DOI：10.1137/060657285

• structured matrix
• matrix approximation
• linearized inverse scattering
• Tikhonov regularization
• image reconstruction

We present a novel method by which the large dense forward matrix A involved in a linear inverse diffusion problem can be decomposed into a number of sparse easily computed matrices. We begin by introducing an errorless decomposition which is applicable to a wide array of such imaging problems. Next, we incorporate interpolation into the construction of the matrices to reduce the computational complexity involved in the matrix- vector multiplications necessary to obtain an inverse solution. Error and computational complexity analysis are provided to support these developments. We then present numerical results that illustrate the gain in computational effciency when the approximation is used in the Tikhonov regularized inverse problem, and show that the use of the approximation has virtually no negative effect on the quality of the reconstructed images. Finally, we discuss applicability to other imaging problems.

• 出版日期2007
• 单位东北大学