Exact multichannel deconvolution on radial domains

A novel multisensor approach to deconvolution is developed. This theory circumvents the ill-posedness inherent in convolution equations by overdetermining the input signal by a multichannel system of convolvers {μ_i}, chosen so that any information lost by one channel is retained by another. The deconvolution problem is then solved by constructing “deconvolvers” that allow us to construct the Dirac δ by filtering each μ_i by its deconvolver, and then adding the filtered channels together. This in turn allows us to reconstruct the original signal f. The process is linear and stable with respect to noise. The general multichannel theory is discussed. The deconvolution theory in radially symmetric domains is then developed in greater detail