This weekend and next, Austin has its annual East Art Studio Tour. I bought this shirt at Art.Science.Gallery. I liked that the shirt was actually mathematical. Art.Science.Gallery is also in danger of closing and is looking to raise funds, so please visit their website to see how you can help.
You may have seen braille in elevators and on ATMs and door signs, but brushed it off as a rudimentary guide for blind people. As a math student, you may have seen braille in a homework problem involving patterns and binary choices. As a puzzle enthusiast, you may have seen braille in a decryption challenge. But is that all to braille?
For an upcoming Toastmasters speech, I decided to get to know braille, by researching and interviewing locals who professionally work with people who are blind and visually impaired. Surprisingly, the more I looked into braille, the more I realized its diminishing role in the modern world. I want to address the problem today.
Last time, we considered the linear equations and linear inequalities that the solution of a nonogram must satisfy. Let us now solve the minimization problem and see how well compressive sensing works. I will consider several examples, then offer a simple fix for the problems that we will encounter.
We know how to represent the solution of a nonogram as a sparse vector . Let us now design the constraints; they will be linear equations and linear inequalities that the entries of must satisfy according to the nonogram. The only information that the nonogram provides are the row and column sequences, so we want to make the most of it. Afterwards, we obtain the sparse vector by minimizing its 1-norm under these constraints. I will discuss the code and the results in the next and final post.
3. Introducing compressive sensing
Today, we will consider how to turn the solution of a nonogram into a sparse vector. But first, let me take a detour and illustrate an approach that Oscar and I initially had considered and comment on its strengths and weaknesses in solving the puzzle.
Throughout our discussion, we will consider the stylish lambda example: