When does a screen reader read alt-text twice?

If I have a link with the image and the text in the link tag and the alt-tag “Level Access Home” and the link text “Level Access Home” it’s going to be read twice. In this case I want to make sure the image is made as a decorative image, it's not a meaningful image at that point because we have the meaningful text. There is another way to do this is you have a link with the image, you can separate the link and the image physically through a div or a table. You don’t want to have those things read twice. In this case we want to make the picture decorative, so we can add a negative tab index so a keyboard user won’t focus on the image and will only focus on the link.