Dre posted on Instagram that he expects to be out of Cedars-Sinai Medical Center soon.
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"Thanks to my family, friends and fans for their interest and well wishes. I'm doing great and getting excellent care from my medical team. I will be out of the hospital and back home soon. Shout out to all the great medical professionals at Cedars. One Love!!"
Media reports indicated the rapper, born Andre Young, was hospitalized this week with what appeared to be a brain aneurysm. At one point he was in an intensive care unit but was now described as being in stable condition, the Los Angeles Times reported.
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Fellow artists were sending well wishes his way.
"Dre is recovering nicely," LL Cool J tweeted.
Ice Cube, who cofounded N.W.A. with Dre, tweeted: "Send your love and prayers to the homie Dr. Dre."
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Missy Elliott wrote: "Prayers up for Dr. Dre and his family for healing & Strength over his mind & body."
And Snoop Dogg wrote on Instagram: "Get well Dr. Dre we need u cuz"
The Compton-born rapper first came to prominence as a cofounder of the pioneering gangsta rap group N.W.A.
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He later launched a successful solo career with "The Chronic," one of the top-selling albums in 1993 that also won him a Grammy.
Dr. Dre also became a successful producer, helping to launch the careers of artists such as Eminem and 50 Cent.
He then became an entrepreneur, working with record executive Jimmy Iovine to release the highly successful headphone company Beats, which was later bought by Apple for $3 billion.
Dre married Nicole Young in 1996 but the couple are currently in the middle of contentious divorce proceedings.