Export sentinel 1 to JPEG but didn't has a projection

Well if you want to view it in a GIS software then as you mentioned you need geocoding. So you need to export it in a format that is supported by ArcGIS. This is why I suggested Geo-Tiff. Another option would be KML.

See here for more ArcGIS supported formats.

You could also take a look at this discussion which suggests you could just import the .img and .data.

Do not forget to share what worked for you so others can benefit.

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