Sometimes I lose track of this, but Compressed Sensing is really about acquiring a sparse signal with the help of an incoherent basis. While much of the emphasis is rightfully about reconstruction work, we are beginning to see the emergence of other tools that complete this framework. Two other stages are emerging:
- the search for bases or dictionaries in which a set of signals are sparse in and,
- specific incoherent measurements tools.
- Multiscale sparse image representation with learned dictionaries
- Efficient sparse coding algorithms
- Non-negative Sparse Modeling of Textures (NMF)
Non Adaptive Measurement codes/matrices (the first four are pasted from Terry Tao site):
Other recent implementations achieving specific goals (sparsity,....)
Random Fourier Ensemble: The signal is a discrete function f on Z/NZ, and the measurements are the Fourier coefficients at a randomly selected set Omega of frequencies of size M ( A is an M x N matrix.) Gaussian ensemble: A is an M x N matrix (M x N Gaussian variables). Bernoulli ensemble: A is an M x N matrix (M x N Bernoulli variables). Gaussian ensemble: A is an m x n matrix (m > n) whose measurement coefficients are Gaussian variables.
- Sparse Measurement Matrix (implementation is mine, but real code available from the authors).
- Random Filters (from here)
Reconstruction codes - Matching Pursuit/Greedy, Basis Pursuit/Linear Programming, Bayesian -
- ell-1 LS: Simple Matlab Solver for ell-1-Regularized Least Squares Problems
- MPTK: Matching Pursuit Toolkit
- Bayesian Compressive Sensing
- SPGL1: A solver for large scale sparse reconstruction
- Chaining Pursuit
- Regularized OMP
- Lp_re, Reweighted Lp - This my implementation but a better one might be available from the authors.
[ Update: some of the homemade codes are here]
Credit: I have cut and pasted section of this entry directly from the Rice repository, Terry Tao site. NASA Mars rover Opportunity on Sol 1432.