Maximum likelihood estimator for noisy input

Suppose we model the measurements by:
begin{equation}
y_k = (underline{x}_k + underline{epsilon}_k)^T underline{a} + v_k, k = 1,…,n
end{equation}

where $v_k$ is zero mean white Gaussian noise with variance $sigma_v^2$ and $underline{epsilon}_k$ is an iid sequence of zero mean Gaussian px1 random vectors with diagonal covariance matrix $sigma_{epsilon}^2I_p$. I try to find MLE of $underline{a}$. Any idea about how to start this problem?

c# – Unity Texture2DArray is too noisy

I’ve generated a Texture2DArray from array of Texture2Ds and for some reason, when my shader is using Texture Array the output colors are noisy, almost as if noise filter was applied on them. Compare,

Just Texture2D:
enter image description here

And when using Texture2DArray:
enter image description here

I generate array using this code:

        Texture2D sample = materials(0).albedo;
        materialArray = new Texture2DArray(sample.width, sample.height, 
        materials.Count * 4, TextureFormat.RGBA32, false);

        for (int i = 0; i < materials.Count; i += 4)
        {
            T_Material material = materials(i);

            materialArray.SetPixels(material.albedo.GetPixels(), i);
            materialArray.SetPixels(material.normal.GetPixels(), i + 1);
            materialArray.SetPixels(material.occulusion.GetPixels(), i + 2);
            materialArray.SetPixels(material.rougness.GetPixels(), i + 3);

        }
        materialArray.Apply(true);
        AssetDatabase.CreateAsset(materialArray, "Assets/_Generated/" + "terrainTextures.asset");
        AssetDatabase.SaveAssets();

Initial Texture2Ds are in RGBA 32bit format:

enter image description here

Generated Texture2DArray (4 Textures, albedo, normal, AO, roughness, But I am only using albedo in shader for now):

enter image description here

My shader is simple, it extracts color data from Texture2DArray using index and applies it to PBR’s albedo input.

enter image description here

And yes, I tried without my special blending effects, just inserting RGBA4 output to Albedo input of PBR both from Texture2DArray sampler and directly from Texture2D sampler.

Results were the same, Texture2DArray is noisy!

Thanks for any help!

sony – I am shooting video at 200 ISO but the video is still really noisy. Any ideas on how to fix this?

Noise is not caused by a certain ISO setting. High ISO isn’t really what causes increased noise. The lower amount of light we usually allow into the camera when using higher ISO is what causes noise. If you limit the light to the same level at ISO 100 that you would use to properly expose for, say ISO 3200, and then try to boost those almost black shadows by five stops in post, you’ll see the same thing as using ISO 3200 with the same exposure time (Tv) and aperture (Av) when shooting.

For more, please see:

Why would using higher ISO and faster shutter speed yield more noise than using lower ISO and slower shutter speed?

Should higher ISOs really be preferred (all other things being equal)?

Regardless of whether you are shooting still images or video, if you want to decrease the amount of noise in a shot you need to increase the amount of light you’re letting into the camera. The options you have for doing this are:

  • Use a wider aperture
  • Use a longer exposure time
  • Add light to the scene

noise – Very noisy image, looks like stars

Yesterday I did some long exposure shots, and it turned out to go quite well (in my opionion), just one issue is that the image is very noisy like I’ve never seen before. The noise looks like stars, and in the sky it looks okay. However stars on the groud is ugly.

Any tips for fixing this? Shot in 1600 ISO (max on my camera).
Image size is decreased to fit into Stackexchange, hopefully they are still visable Noise image

automobiles – Which countries don’t have a strong “car culture” (noisy cars & bikes)?

I currently live in Wales. Like most of the UK, it has a very high rate of people driving extremely loud cars and motorbikes, at all times of the day. Like a lot of people, the noise annoys me, but the police do nothing.
It’s like this in many other countries, i.e. Germany.

So my question is, which countries don’t have a high incidence / culture of people driving loud cars, whilst also being relatively well populated? (whilst Greenland would probably not have this, it’s also not a very practical country to live in). Thanks.

information theory – Shared randomness does not increase capacity of a noisy channel – Why?

Why is it the case that when Alice and Bob use a noisy channel for communication, the capacity of the channel does not increase even if they are allowed to share pre-distributed randomness?

This is mentioned in some notes (see paragraph before Section 4 of https://cds.cern.ch/record/613098/files/0304102.pdf) but I have not seen a proof or an intuitive argument for it yet. Any reference to where this is covered would also be appreciated!

approximation – Best algorithm / method to determine path length from noisy GPS points

i am analyzing a series of GPS points (with time stamps) which are noisy meaning have an accuracy of about 15 meter radius (sometime even more), and i need to extrapolate the distance the vehicle has gone via those GPS points, what is a good algorithm / method to solve such issues ?

Is there a workaround against a noisy soundtrack of a .mp4 video loaded on youtube?

I made an experimental video in “Filmora” and then converted it to .MP4 format (conversion done by Filmora).

This is the video:

The .MP4 file plays well directly from my laptop. The sound has no distortion. Unfortunately, after downloading the video on Youtube the sound becomes bad, there is a lot of noise, parasites, also I play the video with the same computer and the internet speed is good.

Do you know what can be done to get rid of this noise?

(Note: Please do not comment on the content of the video.)

catalina – Macbook pro 16 inch 2019 noisy display in chrome after waking up from sleep

I have this issue sometimes when my mac is waking up from sleep. Some applications like Google Chrome
A part or whole of the application is turning into a noise picture and until I restart the system, it won’t fix.

In this screenshot I have opened inspect view of google chrome. In some websites, one part or whole of the website also, is being displayed like this.

I’ve updated to the latest version of Mac (Catalina 10.15.7) and chrome (86.0.4240.183 (Official Build) (x86_64)). Also this issue is happening when I use the main display or external display too. No differences.

enter image description here

list manipulation – Plotting Noisy Experimental data

I want to plot experimental data (from the atomic absorption), but it is hard to make smooth the data.

Here is the sample model (because of the large file).

data6 = << "https://pastebin.com/raw/t2yf551A";

ListContourPlot(data6
 , ColorFunction -> (ColorData("TemperatureMap")(
     Rescale(#, {0.4, 1})) &), ColorFunctionScaling -> False, 
 ClippingStyle -> Automatic, Contours -> 30, ImageSize -> 800, 
 AspectRatio -> 1, InterpolationOrder -> 3)

enter image description here

My theory predicts the plot such that,

enter image description here

I am seeing kind of matching behavior, but due to the noise, it is hard to make any point. Especially, the data near x=0, there is a sharp change, so my interpolation failed to capture the behavior.

Just in case, here is original data from google drive,

hhh1i = Interpolation(RandomSample(data4, 30000))
data6 = Select(
   Flatten(
    Table({x - y, y, 
      hhh1i(57.14285714285714` (0.775` + 1.` x), y)}, {x, -0.8, 0.8, 
      0.01}, {y, -0.4, 0.8, 0.01}), 1)
   , -0.2 < #((1)) < 0.2 && -0.4 < #((2)) < 0.6 &);