  Iterative deblurring, notably the Richardson-Lucy algorithm with and without
regularization, is analyzed in the context of nuclear and high-energy physics
applications. In these applications, probability distributions may be
discretized into a few bins, measurement statistics can be high, and instrument
performance can be well understood. In such circumstances, it is essential to
understand the deblurring first without any explicit noise considerations. We
employ singular value decomposition for the blurring matrix in a low-count
pixel system. A strong blurring may yield a null space for the blurring matrix.
Yet, a nonnegativity constraint for images built into the deblurring may help
restore null-space content in a high-contrast image with zero or low intensity
for a sufficient number of pixels. For low-contrast images, the control over
null-space content may be gained through regularization. When the
regularization is applied, the blurred image is, in practice, restored to an
image that is still blurred but less than the starting one.
