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
- 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: