506 research outputs found
The Arithmetic Cosine Transform: Exact and Approximate Algorithms
In this paper, we introduce a new class of transform method --- the
arithmetic cosine transform (ACT). We provide the central mathematical
properties of the ACT, necessary in designing efficient and accurate
implementations of the new transform method. The key mathematical tools used in
the paper come from analytic number theory, in particular the properties of the
Riemann zeta function. Additionally, we demonstrate that an exact signal
interpolation is achievable for any block-length. Approximate calculations were
also considered. The numerical examples provided show the potential of the ACT
for various digital signal processing applications.Comment: 17 pages, 3 figure
Robust Image Watermarking Using Non-Regular Wavelets
An approach to watermarking digital images using non-regular wavelets is
advanced. Non-regular transforms spread the energy in the transform domain. The
proposed method leads at the same time to increased image quality and increased
robustness with respect to lossy compression. The approach provides robust
watermarking by suitably creating watermarked messages that have energy
compaction and frequency spreading. Our experimental results show that the
application of non-regular wavelets, instead of regular ones, can furnish a
superior robust watermarking scheme. The generated watermarked data is more
immune against non-intentional JPEG and JPEG2000 attacks.Comment: 13 pages, 11 figure
Wavelet Analysis in a Canine Model of Gastric Electrical Uncoupling
Abnormal gastric motility function could be related to gastric electrical
uncoupling, the lack of electrical, and respectively mechanical,
synchronization in different regions of the stomach. Therefore, non-invasive
detection of the onset of gastric electrical uncoupling can be important for
diagnosing associated gastric motility disorders. The aim of this study is to
provide a wavelet-based analysis of electrogastrograms (EGG, the cutaneous
recordings of gastric electric activity), to detect gastric electric
uncoupling. Eight-channel EGG recordings were acquired from sixteen dogs in
basal state and after each of two circular gastric myotomies. These myotomies
simulated mild and severe gastric electrical uncoupling, while keeping the
separated gastric sections electrophysiologically active by preserving their
blood supply. After visual inspection, manually selected 10-minute EGG segments
were submitted to wavelet analysis. Quantitative methodology to choose an
optimal wavelet was derived. This "matching" wavelet was determined using the
Pollen parameterization for 6-tap wavelet filters and error minimization
criteria. After a wavelet-based compression, the distortion of the approximated
EGG signals was computed. Statistical analysis on the distortion values allowed
to significantly () distinguish basal state from mild and severe
gastric electrical uncoupling groups in particular EGG channels.Comment: 18 pages, Fixed equation (6). arXiv admin note: substantial text
overlap with arXiv:1502.0023
Efficient Computation of the 8-point DCT via Summation by Parts
This paper introduces a new fast algorithm for the 8-point discrete cosine
transform (DCT) based on the summation-by-parts formula. The proposed method
converts the DCT matrix into an alternative transformation matrix that can be
decomposed into sparse matrices of low multiplicative complexity. The method is
capable of scaled and exact DCT computation and its associated fast algorithm
achieves the theoretical minimal multiplicative complexity for the 8-point DCT.
Depending on the nature of the input signal simplifications can be introduced
and the overall complexity of the proposed algorithm can be further reduced.
Several types of input signal are analyzed: arbitrary, null mean, accumulated,
and null mean/accumulated signal. The proposed tool has potential application
in harmonic detection, image enhancement, and feature extraction, where input
signal DC level is discarded and/or the signal is required to be integrated.Comment: Fixed Fig. 1 with the block diagram of the proposed architecture.
Manuscript contains 13 pages, 4 figures, 2 table
A Single-Channel Architecture for Algebraic Integer Based 88 2-D DCT Computation
An area efficient row-parallel architecture is proposed for the real-time
implementation of bivariate algebraic integer (AI) encoded 2-D discrete cosine
transform (DCT) for image and video processing. The proposed architecture
computes 88 2-D DCT transform based on the Arai DCT algorithm. An
improved fast algorithm for AI based 1-D DCT computation is proposed along with
a single channel 2-D DCT architecture. The design improves on the 4-channel AI
DCT architecture that was published recently by reducing the number of integer
channels to one and the number of 8-point 1-D DCT cores from 5 down to 2. The
architecture offers exact computation of 88 blocks of the 2-D DCT
coefficients up to the FRS, which converts the coefficients from the AI
representation to fixed-point format using the method of expansion factors.
Prototype circuits corresponding to FRS blocks based on two expansion factors
are realized, tested, and verified on FPGA-chip, using a Xilinx Virtex-6
XC6VLX240T device. Post place-and-route results show a 20% reduction in terms
of area compared to the 2-D DCT architecture requiring five 1-D AI cores. The
area-time and area-time complexity metrics are also reduced by 23% and
22% respectively for designs with 8-bit input word length. The digital
realizations are simulated up to place and route for ASICs using 45 nm CMOS
standard cells. The maximum estimated clock rate is 951 MHz for the CMOS
realizations indicating 7.60810 pixels/seconds and a 88
block rate of 118.875 MHz.Comment: 8 pages, 6 figures, 5 table
VLSI Computational Architectures for the Arithmetic Cosine Transform
The discrete cosine transform (DCT) is a widely-used and important signal
processing tool employed in a plethora of applications. Typical fast algorithms
for nearly-exact computation of DCT require floating point arithmetic, are
multiplier intensive, and accumulate round-off errors. Recently proposed fast
algorithm arithmetic cosine transform (ACT) calculates the DCT exactly using
only additions and integer constant multiplications, with very low area
complexity, for null mean input sequences. The ACT can also be computed
non-exactly for any input sequence, with low area complexity and low power
consumption, utilizing the novel architecture described. However, as a
trade-off, the ACT algorithm requires 10 non-uniformly sampled data points to
calculate the 8-point DCT. This requirement can easily be satisfied for
applications dealing with spatial signals such as image sensors and biomedical
sensor arrays, by placing sensor elements in a non-uniform grid. In this work,
a hardware architecture for the computation of the null mean ACT is proposed,
followed by a novel architectures that extend the ACT for non-null mean
signals. All circuits are physically implemented and tested using the Xilinx
XC6VLX240T FPGA device and synthesized for 45 nm TSMC standard-cell library for
performance assessment.Comment: 8 pages, 2 figures, 6 table
Fast Matrix Inversion and Determinant Computation for Polarimetric Synthetic Aperture Radar
This paper introduces a fast algorithm for simultaneous inversion and
determinant computation of small sized matrices in the context of fully
Polarimetric Synthetic Aperture Radar (PolSAR) image processing and analysis.
The proposed fast algorithm is based on the computation of the adjoint matrix
and the symmetry of the input matrix. The algorithm is implemented in a general
purpose graphical processing unit (GPGPU) and compared to the usual approach
based on Cholesky factorization. The assessment with simulated observations and
data from an actual PolSAR sensor show a speedup factor of about two when
compared to the usual Cholesky factorization. Moreover, the expressions
provided here can be implemented in any platform.Comment: 7 pages, 1 figur
Fragile Watermarking Using Finite Field Trigonometrical Transforms
Fragile digital watermarking has been applied for authentication and
alteration detection in images. Utilizing the cosine and Hartley transforms
over finite fields, a new transform domain fragile watermarking scheme is
introduced. A watermark is embedded into a host image via a blockwise
application of two-dimensional finite field cosine or Hartley transforms.
Additionally, the considered finite field transforms are adjusted to be number
theoretic transforms, appropriate for error-free calculation. The employed
technique can provide invisible fragile watermarking for authentication systems
with tamper location capability. It is shown that the choice of the finite
field characteristic is pivotal to obtain perceptually invisible watermarked
images. It is also shown that the generated watermarked images can be used as
publicly available signature data for authentication purposes.Comment: 9 pages, 7 figures, 2 table
A Row-parallel 88 2-D DCT Architecture Using Algebraic Integer Based Exact Computation
An algebraic integer (AI) based time-multiplexed row-parallel architecture
and two final-reconstruction step (FRS) algorithms are proposed for the
implementation of bivariate AI-encoded 2-D discrete cosine transform (DCT). The
architecture directly realizes an error-free 2-D DCT without using FRSs between
row-column transforms, leading to an 88 2-D DCT which is entirely free
of quantization errors in AI basis. As a result, the user-selectable accuracy
for each of the coefficients in the FRS facilitates each of the 64 coefficients
to have its precision set independently of others, avoiding the leakage of
quantization noise between channels as is the case for published DCT designs.
The proposed FRS uses two approaches based on (i) optimized Dempster-Macleod
multipliers and (ii) expansion factor scaling. This architecture enables
low-noise high-dynamic range applications in digital video processing that
requires full control of the finite-precision computation of the 2-D DCT. The
proposed architectures and FRS techniques are experimentally verified and
validated using hardware implementations that are physically realized and
verified on FPGA chip. Six designs, for 4- and 8-bit input word sizes, using
the two proposed FRS schemes, have been designed, simulated, physically
implemented and measured. The maximum clock rate and block-rate achieved among
8-bit input designs are 307.787 MHz and 38.47 MHz, respectively, implying a
pixel rate of 8307.7872.462 GHz if eventually embedded in a
real-time video-processing system. The equivalent frame rate is about 1187.35
Hz for the image size of 19201080. All implementations are functional
on a Xilinx Virtex-6 XC6VLX240T FPGA device.Comment: 28 pages, 9 figures, 7 tables, corrected typo
A New Algorithm for Double Scalar Multiplication over Koblitz Curves
Koblitz curves are a special set of elliptic curves and have improved
performance in computing scalar multiplication in elliptic curve cryptography
due to the Frobenius endomorphism. Double-base number system approach for
Frobenius expansion has improved the performance in single scalar
multiplication. In this paper, we present a new algorithm to generate a sparse
and joint -adic representation for a pair of scalars and its application
in double scalar multiplication. The new algorithm is inspired from double-base
number system. We achieve 12% improvement in speed against state-of-the-art
-adic joint sparse form.Comment: 5 pages, 2 figures, 1 tabl
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