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Deep neural network image classifiers are reported to be susceptible to adversarial evasion attacks, which use carefully crafted images created to mislead a classifier. Many adversarial attacks belong to the category of dense attacks, which generate adversarial examples by perturbing all the pixels of a natural image. To generate sparse perturbations, sparse attacks have been recently developed, which are usually independent attacks derived by modifying a dense attack's algorithm with sparsity regularisations, resulting in reduced attack efficiency. In this paper, we aim to tackle this task from a different perspective. We select the most effective perturbations from the ones generated from a dense attack, based on the fact we find that a considerable amount of the perturbations on an image generated by dense attacks may contribute little to attacking a classifier. Accordingly, we propose a probabilistic post-hoc framework that refines given dense attacks by significantly reducing the number of perturbed pixels but keeping their attack power, trained with mutual information maximisation. Given an arbitrary dense attack, the proposed model enjoys appealing compatibility for making its adversarial images more realistic and less detectable with fewer perturbations. Moreover, our framework performs adversarial attacks much faster than existing sparse attacks.