טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKass Merav
SubjectTheoretical Framework for 3D Freehand Ultrasound
Reconstruction Using STLS
DepartmentDepartment of Electrical Engineering
Supervisor Professor Emeritus Arie Feuer
Full Thesis textFull thesis text - English Version


Abstract

3D freehand ultrasound reconstruction is an interesting case of 3D reconstruction from non-uniform sampling. The physician manipulates the ultrasound transducer in a free-hand manner; while non-uniform spread slices (2D Ultrasound images) of the volume are acquired. A magnetic sensor, attached to the transducer, reports the positions of these slices. The reported positions are vulnerable to errors, due to the sensitivity of the magnetic system. The non-uniform recorded data should be used for a 3D grid reconstruction of the scanned volume.

This final paper reviews the work that was done over the last years on this subject. It also offers a theoretical framework for the 3D reconstruction from non-uniform sampling using Structured Total Least Squares (STLS). STLS is an optimization tool for solving over determined linear equation systems. It is based on the known idea of Least Squares (LS). The STLS enables dealing with a more general type of errors in the sampling process than the LS does. It also enables to reduce the number of parameters to be optimized, by capturing the structure of the matrices representing the linear equation system, where by 'structured matrices' we refer to cases of sparse matrices, Toeplitz matrices and so on. This final paper gives a mathematical background on these subjects.

Finally, we present a new algorithm for the reconstruction of 3D freehand ultrasound. We suggest a linear model for the reconstruction, and use the STLS method to find the model parameters. This reconstruction method takes into account not only the gray-level errors in the acquired 2D images (as most existing methods do), but also the errors in the positions of the slices.