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This document summarizes a technique called CADU (collaborative adaptive down-sampling and upconversion) to improve image compression at low bit rates. The technique adaptively decreases high frequency information by directionally prefiltering an image before uniform downsampling. This allows the downsampled image to be conventionally compressed while avoiding aliasing artifacts. At the decoder, the low-resolution image is decompressed and then upconverted to the original resolution using constrained least squares restoration with an autoregressive model. Experimental results show CADU outperforms JPEG2000 in PSNR and visual quality at low to medium bit rates. The technique suggests oversampling wastes resources and could hurt quality given tight bit budgets.
![M.Vijaya Rama Raj, I Kullayamma / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 4, July-August 2012, pp.210-214
Fig. 1. Block diagram of the proposed CADU image compression system.
necessary to low-pass prefilter an input image to half prefiltered image and the original image. The
of its maximum frequency . However, on a illustrated kernel size of the filter is 3. Low-resolution
second reflection, one can do somewhat better. In pixel [black dots in (a)] is the filtered value of the
areas of edges, the 2-d spec- trum of the local image corresponding nine original pixels [white dots in (b)].
signal is not isotropic. Thus, we seek to perform (a) Downsampled prefiltered image; (b) original
adaptive sampling, within the uniform down-sampling image.
framework, by judiciously smoothing the image with
directional low-pass prefiltering prior to down - Most natural images have a rapidly (e.g.,
sampling. exponentially) de- caying power spectrum .
In the directional prefiltering step, the CADU Suppose that the input image is 2-d. in the Fourier
encoder first computes the gradient at the sampled domain and its power spectrum is monotonically
position. Despite its simplicity, the CADU decreasing. Therefore, given a target rate , if the rate-
compression approach via uniform down-sampling is distortion function of the image signal satisfies
๐
not inherently inferior to other image compression D(r*)= ๐ ะค ๐ค ๐๐ค
2
techniques in rate-distortion performance, as long as
then uniform down-sampling by the factor of two will
the target bit rate is below a threshold. The argument
not limit the rate-distortion performance in information
is based on the classical water-filling principle in rate-
theoretical sense. Indeed, our experimental results (see
distortion theory. To encode a set of K Independent
Section IV) demonstrate that the CADU approach
Gaussian random variables {X1, X2,โฆ ,},Xk
outperforms the state-of-the-art JPEG2000 standard in
N(0,๐ k) the rate-distor- tion bounds, when the total the low to medium bit rate range.
bit rate being = ๐ค ๐น ๐ and the total mean-
๐=๐
squares distortion being D= ๐ค ๐ซ ๐ , are given by
๐=๐ III. CONSTRAINED LEAST SQUARES
๐ค ๐ ๐๐๐ CONVERSION WITHAUTOREGRESSIVE
R(D) = ๐=๐
๐ฆ๐๐ฑโก
{๐, ๐๐๐ ๐ ๐ }
๐ MODELING
๐ค
D(R) = ๐ฆ๐ข๐งโก ๐, ๐ ๐ ๐ }
{ In this section, we develop the decoder of
๐=๐
the CADU image compression system.We formulated
the constrained least square problem using two PAR
models of order 4 each: the model of parameters a
and the model of parameters . The two PAR
models characterize the axial and diagonal
correlations, respectively, as depicted in Fig. 4. These
two models act, in a predictive coding perspective, as
noncausal adaptive predictors. This gives rise to an
interesting interpretation of the CADU decoder:
adaptive noncausal predictive decoding constrained
by the prefiltering operation of the encoder.
Therefore the par model parameters a and b
can be estimated from the decoded image by solving
the following least square estimation
Fig: Relationship between the down-sampled
211 | P a g e](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
