Kernel splitting method in support constrained deconvolution for super-resolution
Rémy Prost, Robert Goutte · 2005
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\tauwhere T is the signal support,i_{o}(t)=d^{*-1}(t) * o(t)andg(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.