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Compressive sensing

Introduction:

ˇˇˇˇCompressive sensing (CS) provides a formalized mathematical framework for exploiting the inherently sparse nature of commonly encountered signals and has been the subject of significant activity in recent years. Despite the significant amount of attention that has been given to theoretical aspects of CS, practical image compression is still dominated by JPEG and JPEG-2000. These standards, while exploiting some of the same underlying opportunities for eliminating redundancy as CS, do not specifically take advantage of the theoretical foundations provided by CS.

ˇˇˇˇWe propose a new framework that combines the classical local discrete cosine transform used in image compression algorithms such as JPEG with a global noiselet measure which is solved using second order cone programming (SOCP).

Content:

  • We apply the perspective of a communications system in which knowledge that is shared by both encoder and decoder can be exploited to lower the overall bit rate.
  • We consider quantization, which is inherent in any digital representation of an image.
  • We consider bit rate, which is of course, along with quality, one of the most important determinants of compression algorithm performance.




  • High level illustration of the proposed algorithm. An image is divided into two sets of information at the encoder (left) - an image reconstructed using K1 DCT coefficients (top center) and an image based on K2 noiselet coefficients (bottom center). At the decoder (right) information derived from these two representations is combined to recover the original image via SOCP.



    Demos and Resources:

     


Links: Tsinghua - DCST - HCI&MI


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