Kernel splitting method in support constrained deconvolution for super-resolution

The principle of the method is to split the kernel into two secondary kernels : r(t)=k(t)+d(t), where d(t) must be invertible and satisfy a convergence condition. Then the deconvolution problem is to solve the following equation :
i(t) = i_{o}(t)-\int_{T} i(\tau)g(t-\tau)d\tau
where T is the signal support,
i_{o}(t)=d^{*-1}(t) * o(t)
and
g(t)=d^{*-1}(t)*k(t)
. This equation is solved by using successive substitutions. The deconvolution algorithm may be two steps or iterative and gives a super-resolution. Only the iterative form has been experimented. A noise free restoration of two pulses shows the validity of the method and the convergence speed with different splitting modes. Finally deconvolution from noisy data is studied.