Your code does not work because you want save an array to localStorage. Instead of context.getImageData() you have to use canvas.toDataURL() and then convert dataURL to Base64 string image. After this you can save it to the localStorage.
Your image must be online and in the same domain like your script. It is because of Cross-origin resource sharing (CORS). But if you convert your image like me in dataURL before and then you should not have any problem.
And to localStorage you have today (in 2018) an access only in online mode. Please read:
Full example
See this working example on codepen.io (link to example) because on StackOverflow the snippets are sandboxed and because of this we can not have an access to the localStorage.
var canvas = document.createElement('canvas');
var image = new Image();
var ctx = canvas.getContext('2d');
image.onload = function()
{
    canvas.width = image.width;
    canvas.height = image.height;
    ctx.drawImage(image, 0, 0);
    var dataURL = canvas.toDataURL('image/png');
    var Base64StringImage = dataURL.replace(/^data:image\/(png|jpg);base64,/, "");
    localStorage.setItem('image', Base64StringImage);
    //read from localStorage:
    document.querySelector('img').src = 'data:image/png;base64,' + localStorage.getItem('image');
};
image.src = 'data:image/png;base64,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';
<img src="#">