Only with Arcane Reach
Blasts originate from the caster's square:
A blast fills an area adjacent to you that is a specified number of squares on a side.
Since you are not adjacent to yourself, you cannot target yourself by default.
However, with arcane reach:
Benefit: When using a close arcane attack power, you can choose a square within 2 squares of yours as the origin square. The power still follows the rules for close attacks.
You may absolutely use a square within two squares such that you are caught in the blast. When combined with thunder or psychic resistance, this is a fantastic way to use thunderwave or beguiling strands to rocketjump.