EFFICIENT HARDWARE IMPLEMENTATION OF COMPRESSION ALGORITHMS BASED ON DISCRETE COSINE TRANSFORM AND WAVELETS
The
recent work done by the Joint Photographic Experts Group, most commonly known as
the JPEG group, has introduced a new standard called JPEG 2000 (actually Part I
of JPEG 2000) [1]
for still images. This new standard moves away from transform coding (as
Discrete Cosine Transform, DCT) into the wavelet domain. While several
algorithms have been developed for the new standard, there are several issues
that need to be addressed, mostly efficient hardware implementation of these
algorithms. Although wavelets have been adopted for the new JPEG standard this
is not true for video processing (MPEG-format). This format is still heavily
influenced by transform coding (DCT). The aim of my research is twofold:
efficient hardware implementation for coding Regions of Interest (ROI) for the
new JPEG 2000 standard, and modified our previously adaptive discrete cosine
transform algorithm and make it efficient for hardware implementation.
[1] This work was sponsored by the International Organization for Standardization (ISO), the International Telecommunications Union (ITU), and the International Electro-technical Commission (IEC).
WEIGHTED MEDIAN FILTERS
The image pyramid paradigm provides a computational framework that is well suited for implementing efficient computer vision systems [1-2], [4-5]. This hierarchical structure supports a wide variety of fast and robust algorithms. In the current technical literature, the pyramid paradigm has been approached from two different angles: the linear and the nonlinear. Linear multirate systems have proven to be useful because of their ability to decompose input signals into a set of subband signals. In particular, it has been shown that the subband decomposition can be related to the wavelet transform [4]. On the other hand the nonlinear filtering scheme offers some advantages over linear filtering when the underlying processes are non-Gaussian (image and video processing). There are, however, several aspects of nonlinear pyramid algorithms that warrant further study: i.e. reconstruction algorithms, fast implementation, and detailed comparisons with linear counterparts.
In this research, we propose to analyze subband coding based on the spectral behavior of non-linear filters. The work will be based in a newly discovered tool, namely, "Selection Probabilities" [3]. It has been shown that the linear part of the frequency response of a nonlinear (weighted median) filter can be calculated through these probabilities. The work will emphasize design and characterization on nonlinear filters through these probabilities and comparison with its linear counterpart.
REFERENCES
| [1] | P.J. Burt and E.H. Adelson, ``The Laplacian pyramid as a compact image code,'' IEEE Transactions on Communications, Vol. COM-31, Apr. 1983. |
| [2] | J. Canny, ``A Computational Approach to Edge Detection,'' IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 8, No. 6, Nov. 1986. |
| [3] | M. Prasad and Y.H. Lee, ``Stack Filters and Selection Probabilities,'' IEEE Transactions on Signal Processing, Vol. 42, No. 10, October 1994. |
| [4] | O. Rioul and M. Vetterli, `` Wavelets and Signal Processing,'' IEEE Signal Processing Magazine, October 1991. |
| [5] | A. Witkin, ``Scale Space Filtering,'' in Proc. 8th Int. Joint Conf. Artificial Intelligence, Karlsruhe, 1983, pp. 1019-1022. |
EFFICIENT ALGORITHMS TO CALCULATE THE SAMPLE AND RANK SELECTION PROBABILITIES
Over
the course of last year, we have developed efficient algorithms to calculate
sample and rank selection probabilities [4]. This research has been fruitful
[3]. We propose to continue with the research initiated last year [4] in
algorithms to calculate the sample and rank selection probabilities and further
improve their efficiency. One of the factors that contribute to our approach is
the manner in which the generating functions are calculated. In general, sample
and rank selection probabilities can be calculated from generating function [5]
in terms of binomial polynomials in two dimensions. This approach leads to
matrix convolution [2] or a clever recursive algorithm [1]. With the exception
of [3], these algorithms do not take in account the highly symmetric nature of
binomial coefficients. Using this symmetry, one can save on the order of 50 % of
computations at each step of the algorithm, hence tremendously reducing
computational expenses. In summary, in this research, we propose to modify
present algorithms [3-4] to improve their computational efficiency by at least
an order of magnitude.
REFERENCES
| [1] | S. Again, J. Astola and K. Egiazarian, Binary Polynomial Transforms and Nonlinear Digital Filters, Marcel Decker, Inc, 1995. |
| [2] | K. Egiazarian, P. Kuosmanen, and J. Astola, Boolean Derivatives, Weighted Chow Parameters and Selection Probabilities of Stack Filters, IEEE Transactions on Signal Processing, 44(7), 1996. |
| [3] | A. Morales, E. Boman and S.J. Ko, ``An Efficient Algorithm to Calculate the Sample and Rank Selection Probabilities,’’ Proc. of the 2000 Conference on Information Sciences and Systems, Princeton University, N.J., March 2000. |
| [4] | A. Morales, “Efficient Algorithms to Calculate the Sample and Rank Selection Probabilities”, RDG proposal 1999. |
| [5] | M. Prasad and Y.H. Lee, ``Stack Filters and Selection Probabilities,” IEEE Transactions on Signal Processing, Vol. 42, No. 10, October 1994. |
RESEARCH
IN HIGH DEFINITION TELEVISION (HDTV)
The
purpose of this research was to develop a technology course for EET students that will introduce them to HDTV and allow for reasonable
success in seeking and obtaining a career in industry maintaining HDTV
transmission and reception systems.
Knowledge
required will range from a modest background in digital representation of
analog signals to an extensive understanding of practical diagnosis and
maintenance of signal transmission and reception equipment.
Topics that need to be covered will include: analog to digital signal
conversion, audio and video compression, digital compressed signal decoding, a
comparison to current NTSC TV technology and standards, industry standards and
definitions and their development pertaining to HDTV, a brief overview of
similarities and differences in worldwide implementation of the technology,
hardware diagnosis and repair, transmission system design and implementation.
Most mathematical and basic principles background will be covered in
the regular EET course work.
The major obstacle to this planned course will be the introduction of
transmission of digital signals.
The
recent development of an HDTV transmission standard that is being accepted by
industry is paving the way for implementation of a major change in today's
broadcast television.
Television transmission stations are expected to spend an estimated 7
million dollars apiece just to implement the upgrade.
There will be a large market for technicians familiar with the systems
used and the standards regarding their implementation.
Moreover a new secondary market will be created in the current digital
realm of the World Wide Web and other digital signal carriers.
There will be, without a doubt, a plethora of opportunities in the next
several years.
Basic
skills necessary in the workplace will include the ability to design and
implement a digital broadcast system.
An ability to diagnose and repair the systems involved.
An ability to interpret and implement industry standards, and changes
to these standards.
An ability to address the problems of combined transmission and
reception of both the old technology and new standards simultaneously.
To
this point, two books have been identified as
possible texts for classroom work, however, no ideal text has presented itself.
A current copy of the industry standards pertaining to signal
transmission, audio compression, video compression, and broadcast standards has
been obtained.
Due to its new dynamic nature, this technology is still evolving.
Several, well maintained, Internet sites have been identified as
resources to be used to keep abreast of changes and industry developments.
The most practical classroom materials will be obtained from the HDTV and
AC-3 standards themselves.