How do I upscale an image from 600 x1004 pixels to 1600 x 2560 pixels?

As a practical matter, you cannot add resolution to a placed image with InDesign. Scaling it in InDesign doesn’t add pixels; it stays the same number of pixels. It just distributes them across a larger amount of real estate, lowering the effective resolution of your rescaled image and greatly reducing its reproduction quality. You can’t change that within InDesign per se, but perhaps within Photoshop. You will, of course, have to have Photoshop installed on your system for this to work. If you have the Creative Cloud subscription, Photoshop is another free Adobe program included in the subscription.

Select your placed image within your InDesign document. With the image selected, right-click on it and select Edit Original. This should open your pixel image in Adobe Photoshop. Then choose the Image>Image Size menu command.

• First, ensure that the little chain illustration to the left of your 600 and 1004 Width: and Height: edit boxes shows a linked chain in a gray box. That Constrains Proportions, and lets you scale your image without distorting it. If the chain is not inbound a gray box, click on it to change it that way. 
• Next, change the 600 pixel dimension to 1600. With the Constrain Proportions option selected, you’ll notice that your other dimension automatically changes too: from 1004 to 2677 pixels. Click the OK button.
• That’s more than the 2560 pixels you desired, so you’ll either have to crop the longer dimension down to 2560 in Photoshop after you add the pixels (harder), or crop the image frame within InDesign (easier) to fit the exact size you want the image to be.
• Save the Photoshop file and close it, return to InDesign. If you need to, open the Links panel (Window>Links menu command) and select the Update Links button at the lower right of the Links panel, the one with the two arrows in a circle. Adjust the image frame for your new, larger placed graphic to suit your needs.

Be advised that you’re increasing the size of your current pixel image a lot. Maybe so much that the graphic doesn’t look as good as it did before. You’re asking Photoshop and InDesign to do a lot to make this upscaling of your image happen. Adobe software can make that mechanically possible, but it may or may not make your graphic look better as a result. But you’ll never know until you try.

Good luck,

Randy

Can you please elaborate on what you mean? Does it mean that the image becomes lo-res (pixelated) when you enlarge it?

In this case, the pixel dimensions that you mention are relatively irrelevant.

What’s the image resolution?

If it’s a low-res image (say, 72 ppi) that you enlarge in InDesign by about 2.5 times, then its resolution becomes too low and it looks bad.

You can open the image in Photoshop and upscale it using the Image Size dialog by increasing its resolution, but the quality of results will depend on the original image as well as some other factors. There are also other commercial (and, possibly, free) tools that can upscale image resolution, but you won’t know if the results are satisfactory until you try.

Can you select the image in InDesign and post a screenshot of the Link Info section of the Links panel.