Compressive sampling presentation (Oct 2009)

1. SINGLE –PIXEL IMAGING VIA COMPRESSIVE
SAMPLING
By :-
Ishardeep Singh(0860038)
Manu Mitra (795410)
Srivaths Nadadur (859682)

2. INTRODUCTION
 As we know these days we are looking forward to
rapidly increasing qualities of digital cameras.
 As the number of pixels increases the number of
files also increases that we have to store.
 We use to compress that kind of signal by using
algorithms like JPEG, JPEG-2000 or MPEG.

3. COMPRESSED SAMPLING
 We can recover a signal even if it is under–sampled
 Works on two principles: Sparsity and Incoherence.
 A signal is said to be sparse if it has maximum
coefficients near to zero.

4. INCOHERENCE
 Incoherence says that unlike the signal of interest ,
the sampling waveforms have an extremely dense
representation in Ψ(Collection of columns).
 There is an uncertainty principle while representing
a signal in time domain and frequency domain.
 Example: Impulse function.

5. COMPRESSIVE SENSING
IN ACTION

6. “SINGLE-PIXEL” CS CAMERA

7. SINGLE PIXEL CAMERA ARCHITECTURE

13. ADVANTAGES
 We are getting good quality of image with only a
single photo detector.
 No need to waste our money on high megapixel
cameras for good qualities.
 Single pixel camera will play a vital role in the
development of future cameras.

14. DISADVANTAGES
 It takes much more time to capture an image than
the regular cameras.
 Very new, so reliability is under scanner.

15. CONCLUSION
 Its time to use non- linear sampling theorem(candis-
tao algorithm).
 We can compress the signal at the hardware level.
 The single pixel camera is really efficient and
provides good results at low cost.

16. REFERENCES
 Marco F. Duarte, Mark A. Davenport, Dharmpal Takhar, Jason N.
Laska, Ting Sun, Kevin F. Kelly and Richard G. Baraniuk, Single Pixel
Imaging via Compressive Sampling, IEEE Signal Processing Magazine,
March 2008
 An Introduction To Compressive Sampling by Emmanuel J. Candès
and Michael B. Wakin
 D. Takhar, J.N. Laska, M.B. Wakin, M.F. Duarte, D. Baron, S.
Sarvotham, K.F. Kelly, and R.G. Baraniuk, “A new compressive
imaging camera architecture using
optical-domain compression,” in Proc. Computational Imaging IV, vol.
6065, San Jose, CA, 2006, pp. 43–52.
 E.J. Candès and J. Romberg, “Sparsity and incoherence in compressive
sampling,” Inverse Prob., vol. 23, pp. 969–985, June 2007.
 E.J. Candès, “Lectures on compressive sampling and frontiers in signal
processing,”
The Institute for Mathematics and its Applications. University of
Minnesota, June 2007 [Online]. Available:
http://www.ima.umn.edu/2006- 2007/ND6.4-15.07/abstracts.html