The Bregman method is an iterative method to solve convex optimization problems with equality constraints.

Total variation (TV) denoising, also known as TV regularization or TV filtering, is a powerful technique widely used in various fields, including medical imaging, computer vision, etc. It removes noises while preserving most important structural features. The first image of black hole, captured by Event Horizon Telescope (EHT), was processed and revealed with this technique in 2019.

This post contains some userful tensor notation and tricks which I have seen and collected.

This weekend I learned Preconditioned Conjugate Gradient method with Jonathan Richard Schewchuk’s lecture note “An Introduction to the Conjugate Gradient Method Without the Agonizing Path”. Here I document what I have learned from the note.

Last week I was attempting to implement an in-place fftshift function in c++. I hoped this function could perform shifting along any given dimension of N-dimensional data.

The Moore-Penrose inverse or the pseudoinverse $\mathbf{A}^+ \in \mathbb{R}^{n \times m}$ of a matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$ is a kind of generalization of the inverse matrix to non-square matrices or ill-conditioned matricies. The most confusing part in coding a pinv function is how to choose a appropriate tolerance truncating zero singular values.

I’ve been struggling with calculating the memory usage for a week. Here’s the case: I got a program that needs to estimate how much memory it may consume during runtime with some predefined inputs, such as the size of images, etc. The problem is that the program is so complicated that nearly no one understands the code fully. Not to mention, there are lots of parallel codes in the program, scaling the memory usage by the dynamic number of threads.

I use Visual Studio when I work at the company. Visual Studio does provide a better coding experience on the Windows platform. But honestly, the majority of the coding at the company is just bug fixing, which is less enjoyable.

I used to do all scientific computing work on Jupyter notebooks. My most common way of debugging was print, which is definitely not the best way to do so.