טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNetanel Ratner
SubjectOptimal Multiplexing for Imaging
DepartmentDepartment of Electrical Engineering
Supervisor Full Professor Schechner Yoav
Full Thesis textFull thesis text - English Version


Abstract

Measuring the radiance from several radiation sources is a keystone of imaging processes. It is most useful in a variety of

imaging modalities, e.g. X-ray imaging, spectroscopy, infra-red (IR), multi-spectral imaging etc. Originally utilized for X-ray telescopy, (a.k.a coded aperture imaging) multiplexing is known to be an efficient way of reducing noise in acquisition of directional radiance measurements. Multiplexing, rather than using individual radiation sources in each image acquisition is recognized by a growing number of methods as beneficial. For example, when multiplexing light sources, rather than using each source at a time, the benefits include increased signal-to-noise ratio and accommodation of scene dynamic range.


Existing multiplexing schemes are inhibited by fundamental limits set by noise characteristics and by sensor saturation. The prior schemes, including Hadamard-based codes may actually be counterproductive due to these effects. In our work we derive multiplexing codes that are optimal under these fundamental effects. Thus, the novel codes generalize the prior schemes and have a much broader applicability. Our approach is based on formulating the problem as a constrained optimization.


In the first part of our work, we suggest an algorithm to solve this optimization problem. The superiority and effectiveness of the method is demonstrated in experiments involving object illumination. In the second part of our work we pursue a lower bound on the mean square error (MSE) of the de-multiplexed data as well as the necessary conditions to attain this bound for every desired number of radiation sources. We then analytically find a class of multiplexing codes that follow these conditions and can be used for optimal multiplexing. Our work is also applicable for verifying the optimality of the multiplexing code found be the numerical optimization.