598 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO.

7, JULY 2003

Low-Complexity Transform and Quantization

in H.264/AVC
Henrique S. Malvar, Fellow, IEEE, Antti Hallapuro, Marta Karczewicz, and Louis Kerofsky, Member, IEEE

Abstract—This paper presents an overview of the transform the decoded data in the encoder and decoder). The drift arises
and quantization designs in H.264. Unlike the popular 8 8 from the fact that the inverse transform is not fully specified
discrete cosine transform used in previous standards, the 4 4 in integer arithmetic; rather it must satisfy statistical tests
transforms in H.264 can be computed exactly in integer arith-
metic, thus avoiding inverse transform mismatch problems. The of accuracy compared with a floating point implementation
new transforms can also be computed without multiplications, of the inverse transform (e.g., the inverse discrete cosine
just additions and shifts, in 16-bit arithmetic, thus minimizing transform (IDCT) accuracy specification in H.261 Annex A).
computational complexity, especially for low-end processors. By On one hand, this freedom gives the implementer flexibility
using short tables, the new quantization formulas use multiplica- in adapting to a particular architecture, but in the other hand
tions but avoid divisions.
the cost of this flexibility is the introduction of prediction
Index Terms—Integer transforms, periodic quantization, quan- drift. Several methods have been introduced to control the
tization, transforms, video coding, video standards.
accumulation of drift, ranging from the forced intra refresh
requirements to different oddification techniques [13], [14].
I. INTRODUCTION H.264 makes extensive use of prediction, since even the intra
coding modes rely upon spatial prediction. As a result, H.264 is
T HE NEW H.264 video coding standard provides a com-
pression gain of 1.5
such as
over previous standards
and MPEG-4 Part 2 [1]. The H.264 architec-
very sensitive to prediction drift. In prior standards, prediction
drift accumulation can occur once per P-frame. In contrast, in
H.264 prediction drift can occur much more frequently. As an
ture has many innovations when compared to [2], [3],
illustration, in an I-frame, 4 4 blocks can be predicted from
such as hybrid predictive/transform coding of intra frames and
their neighbors. At each stage prediction drift can accumulate.
integer transforms. In particular, in this paper we review the
For a CIF image, which has a width of 88 4 4 blocks, predic-
new low-complexity transform and quantization approaches
tion drift can accumulate 88 times in decoding one row of an
that are unique to H.264 [4]–[6]. The transforms employ only
I-frame. Thus, it is clear that as a result of the extensive use of
integer arithmetic without multiplications, with coefficients
prediction with H.264, the residual coding must be drift-free.
and scaling factors that allow for 16-bit arithmetic computation
A drift-free decoding design places exacting requirements
on first-level transforms. These changes lead to a significant
upon a decoder implementation, raising the issue of com-
complexity reduction, with an impact in peak signal-to-noise
plexity. Since all decoders must implement the drift-free
ratio (PSNR) of less than 0.02 dB [4]–[7].
inverse transform exactly, the implementation complexity on
In Section II we present the design requirements for the new
any expected decoder architecture (ASIC, media processor,
H.264 transform. In Section III we review basic ideas for integer
DSP, general CPU) must be considered. The algorithm must
transform design and present the length-4 transform adopted in
not place excessive burdens on any expected architecture.
H.264. In Section IV, we consider the quantization procedures,
The main bottlenecks with the inverse transform in the initial
and in Section V we present a design that allows for transform
drafts [2] were the need for 32-bit multiplication and 32-bit
and quantization computations in 16-bit arithmetic. Additional
memory access. A set of criteria were developed to restrict the
aspects are considered in Section VI.
complexity of the inverse transform [13]. Requirements were
using only 16-bit multiplication and 16-bit memory access.
II. DESIGN REQUIREMENTS OF THE H.264 TRANSFORM Two desirable features were an entirely 16-bit implementation;
The structure of H.264 imposes several requirements on even the arithmetic and logic unit (ALU) is 16-bits, and the
the design of residual coding. In traditional work, residual possibility of alternate implementations giving mathematically
decoding contains the possibility of drift (mismatch between exact algorithms. Additionally, memory requirements were also
considered, particularly for inverse quantization and scaling.
Manuscript received April 15, 2003; revised May 9, 2003. An early design feature of H.264 was the variation of the
H. S. Malvar is with Microsoft Research, Redmond, WA 98052 USA (e-mail: quantization step size. The quantization step size increases by
malvar@microsoft.com). approximately 12% for each increase in quantization param-
A. Hallapuro is with the Nokia Research Center, FIN-3372, Tampere, Finland
(e-mail: antti.hallapuro@nokia.com). eter, so that each increment of six in the quantization parameter
M. Karczewicz is with the Nokia Research Center, Irving, TX 75039 USA doubles the quantization step size. This allows a wide range of
(e-mail: marta.karczewicz@nokia.com). quality levels to be addressed efficiently and succinctly. At low
L. Kerofsky is with Sharp Laboratories of America, Camas, WA 98607
(e-mail: lkerofsky@sharplabs.com). quantization, fine quantization control is possible while at high
Digital Object Identifier 10.1109/TCSVT.2003.814964 quantization, coarse quantization is not burdened. During the
1051-8215/03$17.00 © 2003 IEEE
MALVAR et al.: LOW-COMPLEXITY TRANSFORM AND QUANTIZATION IN H.264/AVC 599

development of the transform, the quality range was extended for the frequency index , and sample index
at the low end by making the smallest quantization step size one , with and for . The
quarter of its original value. DCT matrix is orthogonal, that is (where
Currently, H.264 supports 8-bit pixel data. It was expected the superscript denotes transposition).
during the design that support for 10- or 12-bit data will be A disadvantage of the DCT is that the entries are
needed. Initial proposals for higher bit depth were presented in irrational numbers. Thus, in a digital computer, when we com-
[4]. At the time of this writing, there is a call for extensions of pute the direct and inverse transform in cascade, we may not
the bit-depth of H.264 [16]. get exactly the same data back. When we compute
Compression efficiency is the ultimate reason for introducing and , we may not get for
a transform. Thus, the transform must efficiently exploit spatial all if the direct and inverse transforms are implemented in
correlation to aid in compression. As mentioned above, H.264 different machines with different floating-point representations
relies heavily on prediction before the transform. The use of and rounding. If we introduce appropriate scale factors and
4 4 motion segmentation or spatial prediction [2] significantly and define and , then
reduces the spatial correlation between 4 4 blocks, motivating we can make , where is an integer, for almost
the choice of a 4 4 transform. In H.264, the transform codes all by choosing large enough and appropriately. Neverthe-
prediction error signals, which differ from the statistics of nat- less, we cannot guarantee an exact result unless we standardize
ural images often used to justify the selection of a transform. on rounding procedures for intermediate results.
The compression performance of the transform design must be Thus, it is desirable to replace by an orthogonal matrix with
evaluated on segmented prediction error signals. As we discuss integer entries. For that, two basic approaches can be used: one
briefly in Section III, a coding gain analysis [6] has shown that is to build with just a few integers, with symmetries similar to
despite the increased complexity, the discrete cosine transform those of the DCT, to guarantee orthogonality and approximate
(DCT) does not give better compression than the transform se- a uniform frequency decomposition [11], for example [5]
lected.
As we mentioned above, one of the new aspects in H.264 is
the use of a 4 4 transform block size, whereas previous video
(2)
coding standards used the 8 8 DCT. This smaller block size
leads to a significant reduction in ringing artifacts. Compression
gain is improved by using inter-block pixel prediction for intra-
coded frames [2], so that the transform is applied to prediction For the original H.264 design [2], the choices are ,
residuals. With that approach, H.264 intra-frame coding leads , and . That makes quite close to a scaled DCT, and
to better compression than systems based on 8 8 DCT blocks, also ensures all rows have the same norm, because 2
and also better compression than state-of-the-art image coders .
such as JPEG2000 [8]. Another approach is to round the scaled entries of the DCT
The length-4 transform originally proposed in [2] is an integer matrix to nearest integers [6]
orthogonal approximation to the DCT, allowing for bit-exact
implementation for all encoders and decoders, thus solving the (3)
drift problem discussed above. The new transform, proposed in
[4] and adopted in the standard, has the additional benefit of where is the DCT matrix. If we set , then we get
removing the need for multiplications. exactly the same solution as in the original TML design in [2].
For improved compression efficiency, H.264 also employs The main problem with the choice
a hierarchical transform [9] structure, in which the DC coef- is the increase in dynamic range. If , then
ficients of neighboring 4 4 transforms are grouped in 4 4 , i.e., the transform has a dynamic range
blocks and transformed again by a second-level transform. This gain of 52. Since we compute two-dimensional transforms by
hierarchical transform is discussed further in Section VI. transforming rows and columns, the total gain is .
Since , we need 12 more bits to store
than to store . That would lead to the need of 32-bit arith-
III. INTEGER TRANSFORM DESIGN
metic to compute transforms and inverse transforms in the orig-
The DCT [10] is commonly used in block transform coding inal design [2]. To overcome that limitation, we proposed the
of images and video, e.g., JPEG and MPEG, because it is a close matrix obtained by setting in (3), which leads to the
approximation to the statistically optimal Karhunen–Loève new set of coefficients , that is
transform, for a wide class of signals [9], [10]. The DCT
maps a length- vector into a new vector of transform
coefficients by a linear transformation , where the
(4)
element in the th row and th column of is defined by

That way, the maximum sum of absolute values in any row of

(1)
equals 6, so the maximum dynamic range gain increase for a
600 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 7, JULY 2003

2-D transform is , i.e., storage of needs

only six more bits than .
With the design in (4), the rows of are orthogonal but do
not have the same norm. However, that can be easily compen-
sated for in the quantization process, as we discuss in Section IV.
From a compression standpoint, the transform coding gain of
is 5.38 dB, whereas the original TML-1 design or the DCT have
a coding gain of 5.39 dB, for a stationary Gauss-Markov input
with correlation coefficient . Since the input to the trans-
form are prediction residuals, in practice the correlation coeffi-
cient is less than 0.9, so the loss in coding gain is even less than
0.01 dB, which is negligible in practice. Even if inter-block pre-
diction is not used, the 0.01 dB coding gain difference means
that there is no noticeable performance penalty in using the new
design in (4).

A. Inverse Transform
In the decoder, we could use just the transpose of in (4), Fig. 1. Fast implementation of the H.264 direct transform (top) and inverse
as long as we take care of scaling the reconstructed transform transform (bottom). No multiplications are needed, only additions and shifts.
coefficients appropriately, to compensate for the different row
norms. However, in order to minimize the combined rounding IV. QUANTIZATION
errors from the inverse transform and reconstruction, we need
In lossy compression, quantization is the step that introduces
to reduce the dynamic range gain. The problem is in the odd-
signal loss, for better compression. For a given step size ,
symmetric basis functions, whose peak value is two.
usually an integer, the encoder can perform quantization by
Thus, we proposed in [4] scaling the odd-symmetric basis
functions by 1/2; that is, replacing the rows
(7)
and by and
, respectively. That way, the sum of
absolute values of the odd functions is halved to three. Thus, the where and are the row and column indices and con-
maximum sum of absolute values for any basis function now trols the quantization width near the origin (the “dead zone”).
equals four (the sum for the even functions), which reduces The decoder can perform inverse quantization (reconstruction)
the dynamic range gain for the 2-D inverse transform from by simply scaling the quantized data by
to . Since , we reduce the increase in dynamic
(8)
range from 6 bits to 4 bits. The inverse transform matrix is then
defined by [4] A disadvantage of the quantization formula (7) is that it re-
quires integer divisions at the encoder. To avoid divisions, the
original H.264 proposal in [2] replaces the formulas by
(5)

where the tilde indicates that is a scaled inverse of , i.e., (9)

(6) where , the new parameter varies from zero to

, and the association of quantization parameters and
are such that zero corresponds to the finest quantization
The multiplications by 1/2 can be implemented by sign-pre-
and the coarsest quantization. Thus, the parameter
serving 1-bit right shifts [4], so all decoders produce identical
is chosen for fine enough granularity. In the initial proposal in
results. A key observation is that the small errors caused by the
[2], . Note that the dead-zone control parameter
right shifts are compensated by the 2-bit gain in the dynamic
can be set differently for different encoders; it typically lies in
range of the input to the inverse transform.
the range 0 to 1/2. The integer values in the quantization table
Fig. 1 shows flowgraphs of the direct and inverse transforms
and reconstruction table must satisfy
as described above, which are applied to rows and columns
of each 4 4 block. The complexity of these transforms is so (10)
low that the only way to reduce complexity any further would
be to remove the shifts, which would turn the transforms into where is the squared norm of the rows of .
Hadamard transforms [9], [10], with a signifi- In (9), the -bit right shift is equivalent to a division by ,
cant reduction in coding gain and a significant increase in visual thus avoiding an actual division operation. The -bit right shift
coding artifacts. approximates closely a division by , since an -bit shift is
MALVAR et al.: LOW-COMPLEXITY TRANSFORM AND QUANTIZATION IN H.264/AVC 601

actually equivalent to division with rounding toward minus in- for and otherwise,
finity instead of toward zero (the term is an offset that with
minimizes the effect of rounding toward minus infinity). The
values of and are chosen by a compromise: larger values
reduce the approximation error in (10), whereas small values re-
duce the dynamic range of and . In the orig-
inal H.264 design [2], . These values are large
enough so that the error in the AB product is negligible, while
keeping all variables within the limits of 32-bit signed integers. (13)
These matrices were designed to maximize dynamic range and
to satisfy a similar relationship to that in (10), namely
V. 16-BIT ARITHMETIC AND PERIODIC QUANTIZATION TABLES
(14)
Although the quantization formulas in (9) are relatively
simple, we can simplify the implementation complexity further where . The final scaling after reconstruc-
by using formulas that allow for 16-bit arithmetic, with no tion becomes
penalty in PSNR performance. To achieve that goal, we reduce
the values of and the parameters and . (15)
Another aspect of the original H.264 quantization design in
(9) is that the values of increase in approximately equal where .
steps in an exponential scale, roughly doubling for every in- Note that in the final draft standard [3] only the reconstruction
crease of six in . That allows for a closer to linear relationship formulas (12) and (15) are specified, since the standard specifies
between PSNR and the step size control parameter . only the decoder, but not the encoder. Thus, we can look at (11)
By forcing to exactly double for every increase of 6 in as a preferred way of performing quantization, given the require-
[12], we can reduce the size of the quantization and recon- ment of reconstruction via formula (12), which corresponds to
struction tables. That also helps to compensate for the need of formula (8-267) in the draft standard [3]. Similarly, (15) corre-
using three different tables in view of the different row norms sponds to formula (8-278) in the draft standard [3].
of (that need comes from the fact that the 2-D version of (6) With the transform operators defined in Section IV and the
has three different scaling factors: , , and 1/20). quantization and reconstruction formulas above, we see that all
Thus, in our proposal to H.264 [4] we proposed the use of the operations can be computed in 16-bit arithmetic, for input data
following quantization formula: with 9-bit dynamic range. We recall that the inputs to the trans-
form are prediction residuals, and thus they have a 9-bit range
for 8-bit pixel data. There is one exception, though: in the quan-
tization (11), the product has a 32-bit dy-
(11) namic range, but the final quantized value is guaranteed to fall
within a 16-bit range. Analysis of the transform dynamic range
where mod 6 and . We see that for is provided in [17].
every increase of one in the “exponent” , the denominator in
(11) doubles, with no change in the scaling factor multiplying VI. ADDITIONAL ASPECTS
. This periodicity enables us to define a large range The inverse transform and reconstruction specifications in
of quantization parameters without increasing the memory re- H.264 cover additional aspects. For blocks with mostly flat pixel
quirements. The quantization range has been extended relative values, there is significant correlation among transform DC co-
to the original H.264 design. The parameter is chosen by the efficients (i.e., ) of neighboring blocks. Therefore,
encoder, and is typically in the range 0 to 1/2. The corresponding DC coefficients can be grouped in blocks of size 4 4 for the
reconstruction formula that we proposed [4] is luminance channel and blocks of size 2 2 for the luminance
channels. This two-level transformation is usually referred to
as a hierarchical transform [9]. In the original H.264 design
(12) the second-level 4 4 transform was the same as the first-level
transform. The final standard specifies just a Hadamard trans-
where we have explicitly indicated the use of a shift operator to form (that is, the transform in (2) with ), though,
replace multiplication by . because no performance loss was observed over the standard
We note that the quantization and reconstruction fac- video test sets 0, and dynamic range and complexity are re-
tors and depend on the trans- duced.
form coefficient position inside the block. That is With respect to chrominance coding, usually the same step
necessary to compensate for the different scaling factor size as that for luminance is used. However, to avoid visible
in the 2-D version of (6). Their values are given by color quantization artifacts at high quantization step sizes, the
and , current draft limits the maximum value of for chrominance
where for , to about 80% of the maximum value for luminance; according
602 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 7, JULY 2003

to the final draft of the specification the maximum value of is [8] D. S. Taubman and M. W. Marcellin, JPEG2000 Image Compres-
51 for luminance, and 39 for chrominance [3]. sion. Boston, MA: Kluwer, 2002.
[9] H. S. Malvar, Signal Processing With Lapped Transforms. Boston,
In some applications, it is desired to reduce the quantiza- MA: Artech House, 1992.
tion step size to improve PSNR to levels that can be considered [10] K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advan-
visually lossless. To achieve that, the current H.264 draft ex- tages, Applications. Boston, MA: Academic, 1990.
[11] W. Cham, “Development of integer cosine transforms by the principle of
tends the quantization step sizes by two additional octaves when dyadic symmetry,” Proc. Inst. Elect. Eng., pt. 1, vol. 136, pp. 276–282,
compared to the original proposal in [2], redefining the tables Aug. 1989.
and allowing to vary from 0 to 51. Compared to , [12] L. Kerofsky and S. Lei, “Reduced bit-depth quantization,” in Joint Video
Team (JVT) of ISO/IEC MPEG and ITU-T VCEG, Sept. 2001, Doc.
for example, H.264 allows for finer quantization; the minimum VCEG-N20.
in corresponds approximately to in [13] Y. Katayama, “Protection From IDCT Mismatch,” Tech. Rep. MPEG
H.264. For small , additional care must be taken to avoid ex- 93/283, ISO/IEC JTC1/SC2/WG11, 1993.
[14] Yagasaki, “Oddification Problem for IDCT Mismatch,” Tech. Rep.
ceeding the 16-bit dynamic range. Thus the quantization equa- MPEG 93/283, ISO/IEC JTC1/SC2/WG11, 1993.
tion may need to be rescaled, as noted in [3]. [15] L. Kerofsky, “H.26L transform/quantization complexity reduction Ad
During the transform specification, there was an interest in Hoc Report,” in Joint Video Team(JVT) of ISO/IEC MPEG and ITU-T
VCEG, Nov. 2001, Doc. VCEG-O09.
having a matrix-multiply implementation to take advantage of [16] G. Beakley, “Requirement for bit depths above 8 bits,” in Joint Video
the efficient multiply/accumulate architecture of many proces- Team (JVT) of ISO/IEC MPEG and ITU-T VCEG, Mar. 2003, Doc.
sors. Such a definition allows both the efficient shift/add imple- JVT-G044.
[17] L. Kerofsky, “Notes on JVT IDCT,” in Joint Video Team (JVT) of
mentation in Fig. 1 and a separable matrix-multiply implemen- ISO/IEC MPEG and ITU-T VCEG, May 2002, Doc. JVT-C24.
tation that produces identical results. In particular, for mathe- [18] , “Matrix IDCT,” in Joint Video Team (JVT) of ISO/IEC MPEG
matical agreement for low values of the quantization parame- and ITU-T VCEG, Oct. 2002, Doc. JVT-E033r2.
ters, the matrix multiply implementation requires inclusion of
shift and rounding offsets [4], [18].

VII. CONCLUSION Henrique S. Malvar (M’79–SM’91–F’97) received

the B.S. degree from Universidade de Brasília,
We presented the new transform and quantization procedures Brazil, in 1977, the M.S. degree from the Universi-
that have been adopted in the current H.264 draft standard [3]. dade Federal do Rio de Janeiro, Brazil, in 1979, and
the Ph.D. degree from the Massachusetts Institute
The new transform is a scaled integer approximation to the DCT, of Technology (MIT), Cambridge, in 1986, all in
which allows computation of the direct or inverse transform with electrical engineering.
just additions and a minimal number of shifts, but no multipli- From 1979 to 1993, he was on the faculty of
the Universidade de Brasília. From 1986 to 1987,
cations. The basis functions of the new transform do not have he was a Visiting Assistant Professor of Electrical
equal norm, which leads to an increase in the size of the quan- Engineering at MIT and a Senior Researcher at
tization tables. By using an exact exponential scale for the ef- PictureTel Corporation, Andover, MA. In 1993, he rejoined PictureTel, where
was Vice President of research and advanced development. Since 1997, he
fective quantization step size as a function of the quantization has been a Senior Researcher at Microsoft Research, Redmond, WA, where
parameter , the table size is reduced to just 36 16-bit entries. he heads the Communication, Collaboration, and Signal Processing research
The quantization tables are designed to avoid divisions at the group. His research interests include multimedia signal compression and
enhancement, fast algorithms, multirate filter banks, and wavelet transforms.
encoder, and to ensure that data can be processed in 16-bit arith- He has several publications in these areas, including the book Signal Processing
metic. In that way, we achieve a minimal computational com- with Lapped Transforms (Boston, MA: Artech House, 1992).
plexity, with no penalty in PSNR performance. Dr. Malvar is an Associate Editor for the journal Applied and Computational
Harmonic Analysis, an Associate Editor of the IEEE TRANSACTIONS ON SIGNAL
PROCESSING, and a member of the Signal Processing Theory and Methods Tech-
nical Committee of the IEEE Signal Processing (SP) Society. He received the
REFERENCES Young Scientist Award from the Marconi International Fellowship and Herman
Goldman Foundation in 1981. He also received the Senior Paper Award in Image
[1] T. Wiegand and G. Sullivan, “The emerging JVT/H.26L video coding Processing in 1992 and the Technical Achievement Award in 2002, both from
standard,” presented at the Tutorial at ICIP 2002, Rochester, NY, Sept. the IEEE SP Society.
2002.
[2] G. Bjontegaard. Response to call for proposals for H.26L. presented at
ITU-T SG16. [Online]. Available: ftp://standard.pictel.com/video-site
[3] T. Wiegand and G. Sullivan. Draft ITU-T recommendation and final
draft international standard of joint video specification (ITU-T rec.
H.264 j ISO/IEC 14 496-10 AVC. presented at Joint Video Team
(JVT) of ISO/IEC MPEG and ITU-T VCEG. [Online]. Available: Antti Hallapuro was born in Vimpeli, Finland, in
ftp://ftp.imtc-files.org/jvt-experts 1975. He is currently working toward the M.Sc. de-
[4] A. Hallapuro, M. Karczewicz, and H. Malvar, “Low complexity trans- gree at Tampere University of Technology, Tampere,
form and quantization,” in Joint Video Team (JVT) of ISO/IEC MPEG Finland.
and ITU-T VCEG, Jan. 2002, Docs. JVT-B038 and JVT-B039. He joined the Nokia Research Center, Tampere,
[5] A. Hallapuro and M. Karczewicz, “Low complexity (I)DCT,” in Joint Finland, in 1998. At Nokia, he works in the
Video Team (JVT) of ISO/IEC MPEG and ITU-T VCEG, Sept. 2001, Advanced Video Coding Group, where his main
Docs. VCEV-N43. concern is real-time implementation of video coding
[6] H. S. Malvar, “Low-Complexity length-4 transform and quantization algorithms on various processor architectures. He
with 16-bit arithmetic,” in ITU-T SG16, Sept. 2001, Doc. VCEG-N44. has participated in the H.264/MPEG-4 AVC video
[7] G. Bjontegaard, “Calculation of average PSNR differences between codec standardization effort since 2001 and is author
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VCEG, Mar. 2001, Doc. VCEG-M33. group.
MALVAR et al.: LOW-COMPLEXITY TRANSFORM AND QUANTIZATION IN H.264/AVC 603

Marta Karczewicz received the M.S. degree in electrical engineering in 1994 Louis Kerofsky (S’94–M’95) received the B.S.
and the Dr. Technol. degree in 1997, both from Tampere University of Tech- degree in physics and in mathematics from Arizona
nology, Tampere, Finland. State University, Tempe, in 1990, and the M.S. and
During 1994–1996, she was Researcher in the Signal Processing Laboratory Ph.D. degrees in mathematics from the University
of Tampere University of Technology. Since 1996, she has been with the Visual of Illinois, Urbana-Champaign (UIUC), in 1992 and
Communication Laboratory, Nokia Research Center, Tampere, Finland, where 1995 respectively.
she is currently a Senior Research Manager. Her research interests include image At UIUC, he was a Department of Defense
compression, communication, and computer graphics. Advanced Research Fellow during 1991–1994
and a Department of Education Teaching Fellow
during 1990–1991 and 1994–1995. In 1996, he
joined MultiLink, Inc. Andover, MA, as a Software
Engineer, where he contributed to the development of a continuous-presence
video processing system for an H.320-based multipoint conferencing server. In
1997, PictureTel Corp, Andover, MA acquired MultiLink he worked as a Senior
Engineer on digital video processing for server products. In 1999, he joined
Sharp Laboratories of America, Camas, WA, in the Digital Video Department.
He has represented Sharp in ITU-T standardization activities leading to the
standardization of H.264/MPEG-4 AVC where he chaired the ad hoc group on
Transform and Quantization Complexity Reduction. He is currently a Senior
Researcher with interests in video compression, image processing, and fast
algorithms. He has one granted and several pending patents.