Why de-blurring a blurred image is an ill-conditioned problem? What's the intuitive explanation? How to show it using the condition number?

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Deblurring Images: matrices, spectra and filtering, p. 10: "the following properties generally hold for image deblurring problems: [...] The singular values decay to a value very close to zero. As a consequence, the condition number $cond(A) = \sigma_1/\sigma_N$ is very large, indicating that the solution is very sensitive to perturbation and rounding errors". $\endgroup$ – Federico Poloni Mar 30 at 20:37