01439nas a2200145   4500008004100000245008300041210006900124260000900193300001200202490000800214520091600222100001701138700001901155856011901174       2005                        eng d00aA sufficient condition for non-uniqueness in binary tomography with absorption0 asufficient condition for nonuniqueness in binary tomography with  c2005  a335-3570 v3463 a<p>A new kind of discrete tomography problem is introduced: the reconstruction of discrete sets from their absorbed projections. A special case of this problem is discussed, namely, the uniqueness of the binary matrices with respect to their absorbed row and column sums when the absorption coefficient is n=log((1+5^0.5)/2). It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums. Since it has been proved in another paper [A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Linear Algebra Appl. 339 (2001) 171194] that this condition is also necessary, the existence of alternatively corner-connected component in a binary matrix gives a characterization of the non-uniqueness in this case of absorbed projections. <tt> </tt></p>1 aKuba, Attila1 aNivat, Maurice  uhttps://inf.u-szeged.hu/publication/a-sufficient-condition-for-non-uniqueness-in-binary-tomography-with-absorption