Deconvolution for slowly time-varying systems 3D cases

In the present work, we discuss an extension of the deconvolution techniques of Sekko [20] and Neveux [18] to 3D signals. The signals are assumed to be degraded by electronic linear systems, in which parameters are slowly time-varying such as sensors or other storage systems. For this purpose, Sekko & al. [20] developed a structure that has been adapted to time-varying systems [18] in order to produce an inverse filter with constant gain. This latter method was applied successfully to ordinary images [23]. The treatment of omnidirectional images requires working on the unit sphere. Therefore, the problem should be cast in 3D. In the 3D case, the deconvolution method [18] can be applied after some manipulations. The Heinz-Hopf fibration offers the possibility to consider that the sphere is similar to a torus. The advantage of this approach is that Kalman filtering can be applied and omnidirectional images projected on the sphere can be deconvolved.