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Testing results 1:   Rapid  vs  MIT 

Rapid is our new technology on high efficiency image and video acquisition. It accelerates image and video acquisition by 4X faster without loss of image quality. It implements system compression, our own new computing method. The following reported are testing results of Rapid, in comparison with research product of MIT (Massachusetts Institute of Technology), which implements compressed sensing and has been reported on MIT News numerous times. All original image data and MIT results are from MIT News website and thesis report (page 90, Appendix B). While MIT results may take hundreds of seconds in recovery process, the Rapid results only need 0.06 second on a 1.7GHz CPU.

Verification:  To verify, click here to download Rapid Demo (Windows) and the measurement data (image samples) for the Rapid results

(1). Boat 

Original image        MIT result by 25000 measurements
          Original image, 256*256 = 64k                      MIT result,
25k (40%) measurements
                                                                        time = 552 seconds, PSNR = 26.37dB

Rapid result by 17000 measurements
 Rapid result,
17k (25%) measurements
 time = 0.06 second, PSNR = 33.51dB 

(2). Peppers 

Original image     
MIT result by 17000 measurements
         Original image, 256*256 = 64k                           MIT result, 17k (25%) measurements
                                                                          time = 671 seconds, PSNR = 23.56dB

Rapid result by 17000 measurements
  Rapid result, 17k (25%) measurements
 time = 0.06 second, PSNR = 29.34dB

Testing results 2:   Rapid  vs  Rice

The following reported are testing results of Rapid, in comparison with research product of Rice University, called "single-pixel camera", which implements Compressed Sensing and is marketed by InView Technology Corporation. All original image data and the Rice results are from their website http://dsp.rice.edu/cscamera

The Rice results are all produced with 40% partial samples, or called "measurements",  while the Rapid results are all produced with only 25% measurements, nearly half less. For natural images, 25% measurements are usually enough for Rapid to reconstruct a fully sampled image in visually lossless quality. 

We can see that, the Rice results lose color and shape. In stark contrast, Rapid results miraculously achieve visually lossless quality. In addition, Rapid runs thousands times faster than the Rice product in signal recovery. 

Verification:  To verify, click here to download Rapid Demo (Windows) and the measurement data (image samples) for the Rapid results. Click here to see more experimental results by Rice University.

(1). Dice

original image  Rice result by 40% measurements  Rapid result by 25% measurements
  Original image                            Rice result                                 Rapid result

(2). Mandrill

original image  Rice result by 40% measurements  Rapid result by 25% measurements
      Original image                            Rice result                                Rapid result

(3). Mug

original image    Rice result by 40% measurements    Rapid result by 25% measurements
   Original image                     Rice result                           Rapid result

(4). Soccer

original image  Rice result by 40% measurements  Rapid result by 25% measurements
       Original image                       Rice result                                   Rapid result

Testing results 3:   Exact signal recovery

More miraculously, Rapid can exactly recover a high quality signal from its few samples in numerically lossless manner in real time (less than 1 second). This embodies the fundamental difference between System Compression and existing interpolation methods for enhancing signal resolution. The following reported are experimental results of Rapid in exactly recovering high quality signals from their few samples. To verify, click here to download Rapid Demo (Windows) and the full images that can be exactly recovered.

(1).  Birds (768*512*24) can be exactly recovered from 25% samples:

                                                    Birds 25% samples
                                                                                              SamplingExact recovery 
Birds exactly recovered from 25% samples

(2).  Lena (512*512*8) can be exactly recovered from 25% samples:

                                Lena 25% samples
                                            SamplingExact recovery
Lena exactly recovered from 25% samples

(3).  MRI (256*256*8) can be exactly recovered from 25% samples:

                MRI 25% samples
   SamplingExact recovery
Mri exactly recovered from 25% samples

(4).  Soccer (256*256*24) can be exactly recovered from only 5% samples:

                      Dice 5% samples
SamplingExact recovery
Dice full image recovered from 5% samples


1.  Our system compression method makes revolutionary improvement, as compared with compressed sensing theory. System compression fundamentally differs from compressed sensing in both mathematical rationale and technical performance.

2.  Compressed sensing theory relies on signal sparsity and convex optimization as core principles. The sufficiency of sparsity is measured in terms of coherence of an underdetermined system of linear equations. Besides, compressed sensing theory advocates random sampling model for generating the underdetermined system. It claims that its random sampling model were optimal or nearly optimal.

3.  In fact, convex optimization methods such as linear programming and orthogonal matching pursuit execute overly complicated, iterative computations which become very slow and unstable in high dimensional systems. Even worse, the mathematical conditions of compressed sensing impose excessively sparse representations on subject signals, which may severely deteriorate signal quality.

4.  As concrete evidence, demonstrated above are
 the performance of two most representative products of compressed sensing by MIT and Rice University, in comparison with our system compression method which dispenses with both sparse representation and convex optimization.

5.  Clearly, our new method fundamentally improves both signal quality and computing speed. Moreover, system compression forbids random sampling in practice, because it can not yield optimal results at all. Instead, it undermines the chance of real optimal results to be achieved.

6.  The high quality and high speed make system compression a truly applicable method in engineering practice. In o
bjective effect, our system compression method indisputably nullifies compressed sensing theory with overwhelming superiority in technical performance.

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