Unblurring Images – Deconvolution and the Frequency Domain

Don’t trust blurs to hide sensitive information. It is always (partially) reversible.

All experiments are my own, and I’ll go over the basics of deconvolution, Fourier transforms, and why some blur types are ‘safer’ than others!

My aim is to explain things in a simplified and intuitive way, with links to additional sources for those interested in diving deeper.

Is It Real?

Yes – but the success rate depends on the type of blur.

Some are more difficult, like Gaussian, and the Adobe AE Fast Box Blur effect (at default settings).

Others can be unblurred surprisingly well. It’s eerie. For example: Box Blur, Triangle/Hexagon/n-gon Blur, AE Camera Lens Blur, and even optical defocus (depending on the lens).

Compression, noisiness and distortion make the deconvolution process more difficult, but these effects can often be mitigated.

Some blurs destroy more information than others. In the age of surveillance software and machine learning, I think it’s best to assume some information will always be retrievable.

If want to blur a face safely, just slide a fake one underneath :)

Another image blurred by the Captain, with two of my unblur attempts next to it. As you can see, this blur was very destructive. But it seems to be his face!

This challenge has not been solved yet (Feb 28th, 2026).

Image Convolution

To understand unblurring, let’s first look at what a blur actually is. A blur is created by convolving an image.

Simply put, convolution is the process of taking each pixel in an image and blending it with its neighbours. The shape and weights of this neighbourhood is called the kernel.

When all weights in the kernel are positive, the result will be a blur of some kind. The shape dictates the look of the bokeh!

The kernel can be thought of as a stencil, similarly to how the aperture of a real-world camera creates bokeh shapes. Slightly unrelated, but here’s a cool exploration into DIY camera apertures by photographer Jason Yang.

Convolutions don’t always blur, though. If the kernel has negative values (like in the matrices shown below), they can do interesting things like edge detection or sharpening.

Different kernels, from wikipedia

Go watch Captain Disillusion’s video on blur!

And check out 3Blue1Brown’s video on convolution, for a mathematical deep-dive.

The Frequency Domain

An image can be converted to the frequency domain by taking a Fourier transform of it.

The frequency domain is a different perspective of the same image. Instead of seeing it as a grid of pixels, we look at the image’s ‘rates of change’ and we deconstruct the image into a bunch of sine waves. Each individual wave now affects the entire image.

This is useful, because up until this point convolution was a per-pixel operation. When we convert our image to the frequency domain, it becomes a simple multiplication!

The black areas in the frequency domain of a blurred image indicate suppressed high-frequency information.

So in the frequency domain, {Image}_{convolved} = {Image} * {Kernel}. And afterwards, we simply convert back to the Spatial Domain to see the result.

Granted, this may all sound magical and made-up, so here’s a great lecture by Shree Nayar to prove it.

Deconvolution

So blurring is a convolution, which is a multiplication in the frequency domain.

Unblurring (deconvolution) should then be the opposite: a division in the frequency domain! There is a lot more nuance to it, but this is the essence of the process. You take the Fourier transform of your image, and divide it by the Fourier transform of the kernel.

Deconvolving a blur made with a hexagonal kernel.

To find out what the kernel of a specific blur looks like, you can just apply that blur effect to a single white pixel at the center of a black image and dial up the exposure.

For my tests, I rendered a bunch of white pixels with blur effect radii this way, so I can scroll through them and see which give the best results.

The nuances that make deconvolution so difficult with real-world images are mainly:

1. Knowing the exact kernel that was used (it can even be space-variant).
2. Soft kernels suppressing high-frequency information to below the noise floor.

Both require more complex solutions for better results, as well as some trial-and-error.

Soft kernels dampen high-frequency information more, because their frequency domain counterparts are smooth as well. They decay to a level below the noise floor very quickly, making the information nearly impossible to read. Hard kernels translate into ripples in the frequency domain, and those sidelobes let information leak through.

For this reason, it’s a good thing Gaussian blur is one of the most common blur types! But that standard has nothing to do with safety. Its kernel is mathematically separable, meaning it renders fast. And it looks pleasing because of its softness. Here’s a Computerphile video explaining kernel separability.

Other separable kernels usually produce less pleasant-looking blurs (like Box Blur). A hexagonal kernel, which looks more like a true lens defocus than Gaussian does, is not separable and thus expensive – it scales quadratically with its radius: O(r^2).

A directional blur can be deconvolved using a line.
Stock photo by Daniel Thürler on Unsplash.

Two well-known methods of deconvolution are Wiener and Richardson-Lucy.

Wiener Deconvolution uses a noise-to-signal ratio to suppress noise, Richardson-Lucy Deconvolution is an iterative process.

In Conclusion

Use black boxes instead of blurs.

Other common censoring techniques have their own issues. For example, pixelation (mosaic) can be safe, but is problematic when the view is stationary. Or when you know it’s text.

Guessing the text under a mosaic censor
By Dan Petro

I’m a bit cautious about sharing my project files for these experiments. While I didn’t invent the processes, my setup (created with the compositing software Nuke) might make it easier to do this at scale, and I don’t want to facilitate the collecting of sensitive information. Feel free to reach out if you’re a researcher, or a journalist looking to verify my results.