A way to avoid the main HTML to be affected is to create an off-screen canvas that is kept out of the DOM-tree.
This will provide a bitmap buffer and native compiled code to encode the image data. It is straight forward to do:
function imageToDataUri(img, width, height) {
    // create an off-screen canvas
    var canvas = document.createElement('canvas'),
        ctx = canvas.getContext('2d');
    // set its dimension to target size
    canvas.width = width;
    canvas.height = height;
    // draw source image into the off-screen canvas:
    ctx.drawImage(img, 0, 0, width, height);
    // encode image to data-uri with base64 version of compressed image
    return canvas.toDataURL();
}
If you want to produce a different format than PNG (default) just specify the type like this:
return canvas.toDataURL('image/jpeg', quality);  // quality = [0.0, 1.0]
Worth to note that CORS restrictions applies to toDataURL().
If your app is giving only base64 encoded images (I assume they are data-uri's with base64 data?) then you need to "load" the image first:
var img = new Image;
img.onload = resizeImage;
img.src = originalDataUriHere;
function resizeImage() {
    var newDataUri = imageToDataUri(this, targetWidth, targetHeight);
    // continue from here...
}
If the source is pure base-64 string simply add a header to it to make it a data-uri:
function base64ToDataUri(base64) {
    return 'data:image/png;base64,' + base64;
}
Just replace the image/png part with the type the base64 string represents (ie. make it an optional argument).