OPTIMAL TUNING
What is
this?
We
have conducted an extensive computational experiment, lasting multiple
CPU-years, to optimally select parameters for a few important classes
of algorithms for finding sparse solutions of underdetermined systems
of linear equations. The resulting algorithms run ‘out of the box’ with
no user tuning: it is not necessary to select thresholds or know the
likely degree of sparsity. To see our approach you may check here.
Why do it?
Many
of the better known papers in the field of compressed sensing discuss
what can be proved rigorously, using mathematical analysis.
Often, what can be proved is vague (with unspecified constants) or very
weak (unrealistically strong conditions are assumed, far from what can
be met in applications). For practical engineering applications it is
important to know what really happens rather than what can be proved.
Empirical studies provide a direct method to give engineers useful
guidelines about what really does happen. From the theoretical point of
view it will provide us with new and important conjectures to prove.
Which
Algorithms?
We
considered these algorithms:
1. Iterative hard thresholding (IHT) with fixed false alarm rate.
2. Iterative soft thresho soft thresholding (IST) with fixed false
alarm rate.
3. Two stage thresholding (TST). It is a generalization of CoSaMP and
subspace pursuit.
4. Orthogonal matching pursuit (OMP).
5. Least Angle Regression (LARS).
Our Approach in optimizing these algorithms is explained here or in our paper.
Philosophy
of this website.
This
website implements the concept of reproducible research.
The idea is: An article about computational science in a scientific
publication is not the scholarship itself, it is merely advertising
of
the scholarship. The actual scholarship is the complete software
development environment and the complete set of instructions which
generated the figures.
