I don't know how much Miracast (or similar features) deteriorate the original image. So first you'd be better off figuring out the best possible image settings via regular HDMI or DVI-HDMI (I would recommend the latter, but both should be fine), before trying to troubleshoot the Miracast. So next we'll determine whether you're using a native resolution and whether there's unwanted scaling happening in the background.
I'm not sure if you already have a 1080p HDTV, but in any case, the rest of the post is only for that. It most probably won't help with 720p HDTVs, as those are with a 99% certainty not actual 720p panels, but 1366x768 panels. I won't go into further detail as to why it is so, but you can search either the internet or check my old posts if you want more information.
Ok, so:
Go to
http://www.vanity.dk/tft/monitorTest_scale.html and from the top drop-down menu, select "1:1 pixelmapping". If the image is shown as static gray, then you're good to go. The image is actually black and white pixels next to each other, aka. checkerboard pattern. For further confirmation, you can check the image with a magnifying glass. But on the other hand, if you are seeing blotches, artifacts, etc., then you're not operating at the native resolution (1920x1080), or there is scaling happening at some point. And that's the reason you're not getting the optimal image. If you're certain you have a 1920x1080 resolution HDTV, and already checked that the Windows is set for that resolution, then it's a scaling issue.
Few things to check to eliminate scaling:
1) Some HDTVs have a "PC mode" which makes most of the settings right by default. Try that mode.
2) If you're using an AMD GPU, then it will most probably default to an Overscan setting of 10%. You'll have to change that to 0% (via CCC).
3) It might also be your HDTV which is doing the scaling for you. You don't want that. Check for settings that that involve "Unscaled", "Overscan/Underscan", "Aspect ratio", "Stretch", and so on. Check your manual for explanations for settings you're not sure about.
You might also want to check whether your set is using RGB or BGR pixel array. RGB is more common, but for example my set uses BGR. You can make Windows (and at least some of the Linux environments) to take notion of this in font anti-aliasing and ClearType settings, which will make text look better. Default is RGB, so you most probably won't have to change this. But to make sure, you can check your pixel array with a magnifying glass. Pretty self-explanotary, you simply check in which order the red, green and blue sub-pixels are arranged. Check
http://www.lagom.nl/lcd-test/subpixel.php for more info.
The next one doesn't affect text, but you can check for color banding in the vanity-link by selecting "Color range -> Black/blue grad." from the drop-down menu, or from here:
http://www.lagom.nl/lcd-test/gradient.php
If everything is OK, then you should be seeing a smooth gradient from bright to dark. If you can see clear barriers where the color changes to a darker/brighter hue, then you have color banding. The color banding is especially an issue with Philips HDTVs. And the people at Philips seem to be total amateurs at fixing bugs, so there most likely won't be a fix for that in their sets. Ever.
(Especially when also using a Bluetooth mouse keyboard at the limits of range)
