Is it permissible for people to self-impose ashes on Ash Wednesday?

No.

Ashes are meant to be received, not taken and self-imposed. The Ceremonial for Bishops in its explanation of Ash Wednesday states:

On the Wednesday before the First Sunday of Lent the faithful, by receiving ashes, enter upon the season appointed for spiritual purification. This sign of penance, biblical in origin and preserved among the customs of the Church until our own day, expresses the human condition as affected by sin. In this sign we outwardly profess our guilt before God and thereby, prompted by the hope that the Lord is kind and compassionate, patient and abounding in mercy, express our desire for inward conversion. This sign is also the beginning of the journey of conversion that will reach its goal in the celebration of the sacrament of reconciliation during the days leading to Easter.[#253 Ceremonial of Bishops]

The blessing and imposition of ashes should take place either in the Mass or outside of the Mass. In the latter case, it is to be part of a liturgy of the word and conclude with the prayer of the faithful, Blessing and Dismissal. [Circular Letter Concerning the Preparation and Celebration of the Easter Feasts, #21]

The explanation in the Ceremonial of Bishops continues with directives for the Bishop himself to receive the ashes from another minister, concelebrant or deacon.