Hyperspectral images acquired by remote sensing systems are generally degraded by noise and can be sometimes more severely degraded by blur. When no knowledge is available about the degradations present on the original image, blind restoration methods can only be considered. By blind, we mean absolutely no knowledge neither of the blur point spread function (PSF) nor the original latent channel and the noise level. In this study, we address the blind restoration of the degraded channels component-wise, according to a sequential scheme. For each degraded channel, the sequential scheme estimates the blur point spread function (PSF) in a first stage and deconvolves the degraded channel in a second and final stage by means of using the PSF previously estimated. We propose a new component-wise blind method for estimating effectively and accurately the blur point spread function. This method follows recent approaches suggesting the detection, selection and use of sufficiently salient edges in the current processed channel for supporting the regularized blur PSF estimation. Several modifications are beneficially introduced in our work. A new selection of salient edges through thresholding adequately the cumulative distribution of their corresponding gradient magnitudes is introduced. Besides, quasi-automatic and spatially adaptive tuning of the involved regularization parameters is considered. To prove applicability and higher efficiency of the proposed method, we compare it against the method it originates from and four representative edge-sparsifying regularized methods of the literature already assessed in a previous work. Our attention is mainly paid to the objective analysis (via ݈l1-norm) of the blur PSF error estimation accuracy. The tests are performed on a synthetic hyperspectral image. This synthetic hyperspectral image has been built from various samples from classified areas of a real-life hyperspectral image, in order to benefit from realistic spatial distribution of reference spectral signatures to recover after synthetic degradation. The synthetic hyperspectral image has been successively degraded with eight real blurs taken from the literature, each of a different support size. Conclusions, practical recommendations and perspectives are drawn from the results experimentally obtained.