the frequency domain of the frequency domain is just a flipped version of the original image, so that would not work. the idea of frequency-domain based compression is that natural images have little high-frequency information.
As wgj says, it's mainly that Python easily interfaces with other languages without having to copy data. This means that we can use a vast amount of highly efficient mathematical libraries written in C, C++ and Fortran.
NumPy and SciPy are the main workhorses of numerical programming with Python, and provide bindings to extremely efficient libraries (mainly a BLAS and LAPACK implementation), that utilizes SIMD parallelism, adaptive thread parallelism based on workload and cache optimal algorithms to minimise communication between the CPU and RAM.
this gives Python multidimensional arrays that have the flexibility of Python types and speed we can only dream of obtaining if we wrote the low-level code ourselves.
While CHOLMOD is great, you cannot always use the Cholesky factorisation when you solve PDEs. For real-world simulations, we often have to solve systems with hundreds of millions, if not billions, of equations and in then case, even a highly optimised direct solver like CHOLMOD fails. The fill-in simply becomes too large.
For these small test cases, however, simply using CHOLMOD (or any other sparse solver) would do the trick perfectly.
