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 : where T is the signal support, and . 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.