sparse image representation via combined transforms - Convex ...

6.6. SUMMARY OF COMPUTATIONAL EXPERIMENTS 127
6.6 Summary of Computational Experiments
We ran our experiments on an SGI Power Challenger server with 196 MHz CPU. In the
algorithm in Chapter 4, we start with γ =10 2 andstopwithγ =10 5 . Table 6.1 gives
the number of LSQR iterations and the execution time of one iteration in each case. Each
LSQR iteration includes one analysis transform and one synthesis transform of an image.
Since the number of LSQR iterations is machine independent, it is a good criterion for
comparison. The last column lists the total execution time.
Image Size No. of Iterations Execution time of each Total execution
iteration (seconds) time (hours)
Car 64 × 64 226881 0.80 50.2
Pentagon 32 × 32 83928 0.33 7.6
Overlap 32 × 32 104531 0.40 11.7
Separate 32 × 32 266430 0.39 28.9
Table 6.1: Table of Running Times
In the above simulations, the tolerance parameter for LSQR is chosen to be 10 −10 [117].
The minimum tolerance for Newton’s method is chosen to be 10 −7 . (The Newton iteration
will stop if the norm of the gradient vector is less than 10 −7 .)
6.7 Software
We plan to develop a software package (perhaps named “ImageAtomizer”, following Shaobing
Chen’s “Atomizer” package). At present it includes the following directories:
• Datasets—data files of images and of Matlab functions providing access to them.
• MEXSource—CMEX source code for the direct edgelet transform, the fast approximate
edgelet transform, 2-D DCT, and more.
• Methods—Matlab functions carrying out our global minimum l 1 norm algorithm,
Matching Pursuit, Method of Frames, together with some supporting files.
• Transforms—Matlab functions for the curvelet transform, DCT, edgelet, etc.