The wording, "after having received the accurate knowledge [τὴν ἐπίγνωσιν τῆς ἀληθείας] of the truth," is evidently a reference to Christians and apparently encompasses more than just a knowledge of Christ's atoning sacrifice. Such knowledge as spoken of in Epistle to the Hebrews actually entails an intimate acquaintance with many details regarding the Christian faith. The writer of Hebrews certainly does not have unbelievers--ones who have merely been presented with the Gospel--in mind; he is talking about believers, who accurately (i.e. fully and deeply) come to know the truth about God and Christ, then reject such knowledge because they develop a wicked heart lacking faith (Heb 3:12). It is important to note that the author of Hebrews is referring to those who willingly and persistently sin. He is not talking about those Christians who commit transgressions out of ignorance:
"Apostasy can only occur μετὰ τὸ λαβεῖν . . . a condition which is explained in detail in chap. 6 [of Hebrews]. Without this preceding knowledge of the covenant its willful repudiation is impossible. Those spoken of in ver. 25, as having abandoned meeting with their fellow Christians, and possibly as having neglected, if not renounced, the confession of their hope, were perhaps alluded to here, as on their way to apostasy. They are warned that they are drifting into an irredeemable condition, for to those who have repudiated and keep repudiating the one sacrifice of Christ, οὐκέτι περὶ ἁμαρτιῶν ἀπολείπεται θυσία"(Expositor's Greek Testament 4:348).
"It is most important here to keep this cardinal point distinctly in mind; that the Ἐκουσίως ἁμαρτάνοντες are not mere professors of religion, but real converts, or else ver. [Heb 10:29] becomes unintelligible . . ." (Alford's Greek Testament 4:199).
The text is more intelligible if we interpret Heb 10:29 as a reference to a hypothetical apostate Christian. Notice that the writer also uses ἡμῶν in 10:26. How could he be
referring to non-Christians or those who have simply been exposed to the Gospel since he employs ἡμῶν?