Image Processing

Why is Deconvolution Difficult?

Lena convolved with the Airy pattern

When taking a picture with a camera, the “true” image is convolved with the point spread function (PSF) of that camera, potentially producing a blurred image. Deconvolution is the process of removing the effect of this PSF again. In this article, I demonstrate that this is not an easy thing to do… read more

Submitted on 24 December 2013

The Perfect Camera

Airy pattern

The perfect camera is diffraction limited. This article is written strictly from an optical point of view, so don’t expect a Nikon / Canon / Leica comparison here… Optically, a camera (or telescope or other optical instrument) can be described by its point spread function (PSF), which… read more

Submitted on 21 July 2013

Valentine Tomography

Heart

Happy Valentine’s Day! I might not be very romantic, but I had to do something with it. Imaging the heart is an important application of tomography and other techniques in medical imaging. Since hearts are everywhere on Valentine’s Day, let’s scan one. This article builds on… read more

Submitted on 14 February 2013

Tomography, Part 4: Algebra!

The first three articles on tomography focused on analytic techniques, in which the reconstruction problem is attacked using mathematical analysis. When the step to real world scanners is made, the problem is discretized. Both the projections and the reconstruction area are divided into pixels, and a numerical approximation of the true mathematical technique is introduced. The algebraic techniques assume… read more

Submitted on 9 December 2012

Tomography, Part 2: Yes, You Can

Sinograms of box with ball

This article shows that it is possible to reconstruct the inside of a person or object from (lots of) projections of that person or object. Mathematically, tomography is based on the fact that the function values of a two-dimension functional \(f(x,y)\) can be calculated from projections of that function. This basic fact was discovered… read more

Submitted on 11 November 2012

Tomography, Part 1: Projections

Projection of box with ball

Have you ever wondered how a CT (or CAT) scanner creates an image of the inside of a person? The answer is computing. CT and CAT are short for computed (axial) tomography. Computing is the secret sauce that is poured over the hundreds or thousands of X-ray photos that make up a CT scan, to merge them into a single image. This first article on tomography explains projections, the essential input data for tomography… read more

Submitted on 29 October 2012

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