Compressed sensing

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Compressed Sensing or compressed sensing (also sensing compressive , compressive sampling or sparse sampling ) is a method for recording and reconstructing sparse ( English sparse ) signals or information sources. Due to their redundancy, these can be compressed without significant loss of information . This is used efficiently when sampling the signals to significantly reduce the sampling rate compared to conventional methods.

history

The process was invented around 2004 independently of Terence Tao and Emmanuel Candès on the one hand and David Donoho on the other. Importantly compressed sensing especially in image processing , but also in many other fields of digital signal processing.

Applications

The basic idea can be illustrated using the example of a digital camera . A high-resolution image is captured by such a camera with a large number of sensors ( pixels ). The volume of raw data can be several dozen megabytes . This image is then processed using a common image compression process and the data volume is drastically reduced (typically to a tenth or less, as is the case with JPEG files , for example ). Ultimately, a large part of the recorded sensor data is then not used at all. If this information is not even included, must therefore equal to a "compressed sensing" ( English compressed sensing ) of the image is carried out, the hardware can be saved (simpler sensor or cost-effective camera) and be reduced under certain circumstances, the amount of time and energy.

Since the 2010s, for example, single-pixel cameras have been developed that either work without a lens via a locally variable pinhole in a controllable optical grid or work with a rapid sequence of pseudo-random projection patterns in the illumination or imaging beam path. The data must then be computationally combined to form an image of the recorded object space .

literature

  • Gitta Kutyniok: Compressed Sensing PDF; 670 kB accessed on August 28, 2017.

Web links

  • Nadine Christine Fell: Compressed Sensing in Computed Tomography , Master's thesis at Saarland University, Saarbrücken, February 2015, PDF; 10 MB. Retrieved August 28, 2017.

Individual evidence

  1. ↑ T. Tao, E. J. Candès: Near-optimal signal recovery from random projections: universal encoding strategies? , IEEE Transactions on Information Theory, Volume 52, Issue 12, 2006, pp. 5406-5425
  2. ↑ E. J. Candès, J. Romberg, T. Tao: Stable signal recovery from incomplete and inaccurate measurements , Comm. Pure Appl. Math., Vol. 59, 2006, pp. 1207-1223
  3. ↑ D. Donoho: Compressed Sensing , IEEE Transactions on Information Theory, Volume 52, 2006, pp. 1289-1306
  4. ^ Greg Borenstein: Single Pixel Camera , Urban Honking, January 24, 2011, accessed August 29, 2017
  5. ^ Scott Krig: Computer Vision Metrics: Survey, Taxonomy, and Analysis , Page 9: Single-Pixel Computational Cameras , SpringerLink: The Expert's Voice in Computer Vision , 2014, ISBN 9781430259305
  6. ↑ Larry Hardesty: A faster single-pixel camera - New technique greatly reduces the number of exposures necessary for "lensless imaging," MIT News Office, March 29, 2017, accessed August 29, 2017