  We have shown that the vector of the point spread function (PSF)
lexicographical presentation belongs to the left side conjugated null space
(NS) of the autoregression (AR) matrix operator on condition the AR parameters
are common for original and blurred images. The method of the PSF and inverse
PSF (IPSF) evaluation in the basis of the NS eigenfunctions is offered. The
optimization of the PSF and IPSF shape with the aim of fluctuation elimination
is considered in NS spectral domain and image space domain. The function of
surface area was used as the regularization functional. Two methods of original
image estimate optimization were designed basing on maximum entropy
generalization of sought and blurred images conditional probability density and
regularization. The first method uses balanced variations of convolutions with
the PSF and IPSF to obtaining iterative schema of image optimization. The
variations balance is providing by dynamic regularization basing on condition
of the iteration process convergence. The regularization has dynamic character
because depends on current and previous image estimate variations. The second
method implements the regularization of the deconvolution optimization in
curved space with metric defined on image estimate surface. The given iterative
schemas have fast convergence and therefore can be used for reconstruction of
high resolution images series in real time. The NS can be used for design of
denoising bilateral linear filter which does not introduce image smoothing.
