Travis Barker Seen at His Recording Studio 1 Week After Hospitalization for Pancreatitis

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Travis Barker is getting back on his feet after being hospitalized last week.

The Blink-182 drummer, 46, was photographed walking outside his recording studio in Calabasas, California, on Tuesday — exactly one week since he was seen getting wheeled into Cedars-Sinai Medical Center in Los Angeles on a stretcher with wife Kourtney Kardashian by his side.

"He's slowly on the mend and closely following his doctors' orders," a source close to Barker tells PEOPLE.

Barker, who wore black sunglasses to match his T-shirt and pants, previously told his 7.5 million Instagram followers Saturday that he was "much better" after he was hospitalized last week due to pancreatitis, an inflammation of the organ that aids in digestion and regulating blood sugar.

RELATED: Shanna Moakler Speaks Out About Ex Travis Barker's Hospitalization: 'I Pray for a Speedy Recovery'

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"He was complaining of cramps," a source told PEOPLE one day after Barker was seen entering Cedars-Sinai Medical Center.

"Kourtney was worried yesterday. They both were," another source said. "Travis was suffering from extreme stomach pain and could barely walk."

At the time, Barker's daughter Alabama Luella, 16, asked fans to "please send your prayers."

His stepdaughter Atiana De La Hoya, 23, also opened up to her followers, writing on her Instagram Story, "Thank you for the outpouring of love and prayers sent our way at this time. It is heard, felt and appreciated Xx."

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Barker has since updated his fans on his health, writing on his Instagram Story on Saturday, "I went in for an endoscopy Monday feeling great but after dinner, I developed excruciating pain and have been hospitalized ever since."

"During the endoscopy, I had a very small polyp removed right in a very sensitive area, usually handled by specialists, which unfortunately damaged a critical pancreatic drainage tube. This resulted in severe life-threatening pancreatitis," he added. "I am so very very grateful that with intensive treatment, I am currently much better."

Kardashian also shared an update on her own Instagram Story, noting that they were "so touched and appreciative" of the support they received.

RELATED VIDEO: Travis Barker Hospitalized for Pancreatitis After 'Complaining of Cramps': Source

"Oh what a scary and emotional week it has been. Our health is everything and sometimes we take for granted how quickly it can change," Kardashian wrote. "Travis and I went in for a routine endoscopy together and he ended up with severe, life-threatening pancreatitis."

The Poosh founder added that she's "so grateful to God for healing my husband," as well as to their fans' prayers and the specialists, doctors and nurses at Cedars-Sinai Medical Center in Los Angeles "for taking such wonderful care" of them.

"It's crazy how sometimes words could never truly express the gratitude or feelings I have inside of me," Kardashian continued in a follow-up Instagram Story.