The question arises: what is the scope of compressive sensing? What you show is l1 regularization. This has been around far longer than the term 'compressive sensing'. Even the theory underlying it pre-dates 'compressive sensing' [1]. I think the 'compressive' 'sensing' aspect comes about due to the possibility of literally, 'compressively sensing', not just in using 'l1-regularization'.
Further, an ambiguity arises in the concept of the interactive graphics in the OP website: the graphical explanation shown holds not just for 'l1' regularization, but also for say, 'l2' regularization (and other regularizations). The 'bar' could also represent a scaled version of the l2 norm. It is not easily apparent why it should only be 'l1'.
When it comes to graphical intuition for compressive sensing, I find the 'l2-ball' (intersects 'low-dimensional measurements' at dense points ) vs. 'l1-ball' (intersects 'low-dimensional measurement' equations on sparse points in the plane, thus 'promoting sparsity', see for example, [2]) to be more lucid.
Since you already have the excellent interactive web-site, can you possibly include the l1-ball vs. l2-ball [2] graphic?
[1] R. Tibshirani, "The Lasso page "Regression shrinkage and selection via the lasso". Journal of the Royal Statistical Society, Series B 58 (1): 267–288.
[2] R. Baraniuk, "Compressive sensing." IEEE signal processing magazine 24.4 (2007).
Edit:
Another suggestion: The OP website format is a great way to demonstrate the utility of regularizations in optimization, which has wide applications in machine learning, data interpolation, etc.[3]
Thanks for your insightful comment. Our objective in this blab (= Web Lab) was a simple view into CS for the non-specialist, and so we were wary of getting in too deep with the various norms. And, frankly, a toy problem such as this omits a lot of important details. However, representing the l2 norm on the bar plot is a great idea. I'll look into that (BTW, you are free to edit, save & share the blab yourself if you wish.).
For more detail you are welcome to visit "Intuitive Compressive Sensing" http://www.puzlet.com/m/b007z and "Compressive Sensing Primer" http://www.puzlet.com/m/b0080 (these aren't blabs, and rely on server-side computation). In particular, there is an interesting plot in the first link showing the difference in norms.
Side note to everyone on Hacker News: Contributing to Wikipedia is a great way to spread ideas because Wikipedia is a searchable platform that everyone looks at. An informational article that you write for Wikipedia is likely to have far more impact than if you write on your personal blog. So if your goal is to educate, consider contributing!
We are big fans of Wikipedia, and so appreciate your comment. However, even though I am straying from your (valid) point, I think it worth emphasizing that not all types of knowledge are encyclopedic, and encyclopedias do not suit every purpose. Blogs, for instance, can convey a casual interaction and experience with a topic that would not be suitable for wikipedia.
Broadly our goal is to bring code and knowledge together in exciting ways. In this case to attempt to bring an "Aha!" moment to a non-specialist audience. In other cases, people may be served better to get involved with the code: http://puzlet.com/m/b00d3 . Anyway, those are the kinds of areas we want to explore.
Wikipedia is great, but it takes an order of magnitude more effort to create and maintain a wikipedia article than it takes to put the same exact content on your own site.
Further, an ambiguity arises in the concept of the interactive graphics in the OP website: the graphical explanation shown holds not just for 'l1' regularization, but also for say, 'l2' regularization (and other regularizations). The 'bar' could also represent a scaled version of the l2 norm. It is not easily apparent why it should only be 'l1'.
When it comes to graphical intuition for compressive sensing, I find the 'l2-ball' (intersects 'low-dimensional measurements' at dense points ) vs. 'l1-ball' (intersects 'low-dimensional measurement' equations on sparse points in the plane, thus 'promoting sparsity', see for example, [2]) to be more lucid.
Since you already have the excellent interactive web-site, can you possibly include the l1-ball vs. l2-ball [2] graphic?
[1] R. Tibshirani, "The Lasso page "Regression shrinkage and selection via the lasso". Journal of the Royal Statistical Society, Series B 58 (1): 267–288.
[2] R. Baraniuk, "Compressive sensing." IEEE signal processing magazine 24.4 (2007).
Edit:
Another suggestion: The OP website format is a great way to demonstrate the utility of regularizations in optimization, which has wide applications in machine learning, data interpolation, etc.[3]
[3] http://www.mit.edu/~9.520/spring07/Classes/rlsslides.pdf