Some Geometric and Combinatorial Properties of Binary Matrices Related to Discrete Tomography.

Date of Submission

December 2013

Date of Award

Winter 12-12-2014

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Advance Computing and Microelectronics Unit (ACMU-Kolkata)


Bhattacharya, Bhargab Bikram (ACMU-Kolkata; ISI)

Abstract (Summary of the Work)

Digital tomography deals with the problem of reconstructing an image from its projections. The image may or may not be reconstructible uniquely. The effective reconstruction also depends on the kind of projections taken. We consider the simplest two-dimensional case in which we have a 2D matrix and the projections are orthogonal. The matrices which are not uniquely reconstructible are known as ambiguous. In this thesis we concentrate on decomposing such an ambiguous matrix into a minimum number of matrices such that each of them are unambiguous. We claim that the XOR sum of these component matrices would return the original matrix. As the component matrices can be stored just by storing the row-sum and column-sum (the horizontal and vertical projections), we can store any ambiguous matrix by storing the projections of the components. The space management highly depends on the minimum number of components which we define as XORdimension. We study the trend of change in XOR-dimension first for n×n matrices and then for general m × n matrices.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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