Category: Optimization

Inverse Problem (Part 3)

In the two previous posts I wrote about inverse problems (part 1 and part 2). For a proper introduction into inverse problems I refer to these posts. In my last post about inverse problems, I have showed you how to describe a prediction (classification problem) in terms of an inverse problem and how to solve

Inverse Problem (Part 2)

In the last post I have written about inverse problems. A simplified toy example was presented, which showed you how to translate this problem into an optimization problem. Optimization problems can be solved with multiple algorithms, e.g. gradient descent or evolutionary algorithms. This article presents a more sophisticated inverse problem. We want to classify images

Inverse Problem (Part 1)

The process of calculating the causal factors from an observation is called inverse problem. An inverse problem is much harder to solve than the corresponding forward counterpart, which is calculating the observation from the causal factors. Many problems in science and math are inverse problems. They can be found in optics, radar, acoustics, communication theory,

Image deblurring (Part 2)

This article is a follow up to my last article Image debluring (Part 1). There I wrote about the specific problem of image deblurring. The problem is to find the original image, which is convolved with a known point spread function. This can be solved with an interactive optimization procedure. My intention to write about

Image deblurring (Part 1)

Image deblurring is the process of removing artifacts from images. An out of focus camera or movement during the exposure can cause these artifacts. This is often modeled as a convolution of the undistorted image with a point spread function. Deblurring is the inversion of this model. Inverse problems are often solved in an iterative