Its not possible to update using REST, you can try below JSOM code to update its value:
1) Either when you have ID
function updatePublishingImage() {
var clientContext = new SP.ClientContext(siteUrl);
var oList = clientContext.get_web().get_lists().getByTitle('Pages');
var oListItem = oList.getItemById(1);
oListItem.set_item('PublishingPageImage', "<img alt='abc image' src='/sites/test/PublishingImages/abc.jpg'>");
oListItem.update();
clientContext.executeQueryAsync(function(){
console.log("updated image");
},function(){
console.log("something went wrong");
});
}
2) Or when you know the server relative url:
var ctx = SP.ClientContext.get_current();
var file = ctx.get_web().getFileByServerRelativeUrl(url);
ctx.load(file,'ListItemAllFields');
ctx.executeQueryAsync(
function (file) {
var listItem = file.get_listItemAllFields();
listItem.set_item("PublishingPageImage","<img alt='abc image' src='/sites/test/PublishingImages/abc.jpg'>");
listItem.update();
ctx.executeQueryAsync(
function () {
},function(){
});
}, function(){
});