2,276 research outputs found
Multiplierless 16-point DCT Approximation for Low-complexity Image and Video Coding
An orthogonal 16-point approximate discrete cosine transform (DCT) is
introduced. The proposed transform requires neither multiplications nor
bit-shifting operations. A fast algorithm based on matrix factorization is
introduced, requiring only 44 additions---the lowest arithmetic cost in
literature. To assess the introduced transform, computational complexity,
similarity with the exact DCT, and coding performance measures are computed.
Classical and state-of-the-art 16-point low-complexity transforms were used in
a comparative analysis. In the context of image compression, the proposed
approximation was evaluated via PSNR and SSIM measurements, attaining the best
cost-benefit ratio among the competitors. For video encoding, the proposed
approximation was embedded into a HEVC reference software for direct comparison
with the original HEVC standard. Physically realized and tested using FPGA
hardware, the proposed transform showed 35% and 37% improvements of area-time
and area-time-squared VLSI metrics when compared to the best competing
transform in the literature.Comment: 12 pages, 5 figures, 3 table
A Class of DCT Approximations Based on the Feig-Winograd Algorithm
A new class of matrices based on a parametrization of the Feig-Winograd
factorization of 8-point DCT is proposed. Such parametrization induces a matrix
subspace, which unifies a number of existing methods for DCT approximation. By
solving a comprehensive multicriteria optimization problem, we identified
several new DCT approximations. Obtained solutions were sought to possess the
following properties: (i) low multiplierless computational complexity, (ii)
orthogonality or near orthogonality, (iii) low complexity invertibility, and
(iv) close proximity and performance to the exact DCT. Proposed approximations
were submitted to assessment in terms of proximity to the DCT, coding
performance, and suitability for image compression. Considering Pareto
efficiency, particular new proposed approximations could outperform various
existing methods archived in literature.Comment: 26 pages, 4 figures, 5 tables, fixed arithmetic complexity in Table
I
An Orthogonal 16-point Approximate DCT for Image and Video Compression
A low-complexity orthogonal multiplierless approximation for the 16-point
discrete cosine transform (DCT) was introduced. The proposed method was
designed to possess a very low computational cost. A fast algorithm based on
matrix factorization was proposed requiring only 60~additions. The proposed
architecture outperforms classical and state-of-the-art algorithms when
assessed as a tool for image and video compression. Digital VLSI hardware
implementations were also proposed being physically realized in FPGA technology
and implemented in 45 nm up to synthesis and place-route levels. Additionally,
the proposed method was embedded into a high efficiency video coding (HEVC)
reference software for actual proof-of-concept. Obtained results show
negligible video degradation when compared to Chen DCT algorithm in HEVC.Comment: 18 pages, 7 figures, 6 table
Improved 8-point Approximate DCT for Image and Video Compression Requiring Only 14 Additions
Video processing systems such as HEVC requiring low energy consumption needed
for the multimedia market has lead to extensive development in fast algorithms
for the efficient approximation of 2-D DCT transforms. The DCT is employed in a
multitude of compression standards due to its remarkable energy compaction
properties. Multiplier-free approximate DCT transforms have been proposed that
offer superior compression performance at very low circuit complexity. Such
approximations can be realized in digital VLSI hardware using additions and
subtractions only, leading to significant reductions in chip area and power
consumption compared to conventional DCTs and integer transforms. In this
paper, we introduce a novel 8-point DCT approximation that requires only 14
addition operations and no multiplications. The proposed transform possesses
low computational complexity and is compared to state-of-the-art DCT
approximations in terms of both algorithm complexity and peak signal-to-noise
ratio. The proposed DCT approximation is a candidate for reconfigurable video
standards such as HEVC. The proposed transform and several other DCT
approximations are mapped to systolic-array digital architectures and
physically realized as digital prototype circuits using FPGA technology and
mapped to 45 nm CMOS technology.Comment: 30 pages, 7 figures, 5 table
A DCT Approximation for Image Compression
An orthogonal approximation for the 8-point discrete cosine transform (DCT)
is introduced. The proposed transformation matrix contains only zeros and ones;
multiplications and bit-shift operations are absent. Close spectral behavior
relative to the DCT was adopted as design criterion. The proposed algorithm is
superior to the signed discrete cosine transform. It could also outperform
state-of-the-art algorithms in low and high image compression scenarios,
exhibiting at the same time a comparable computational complexity.Comment: 10 pages, 6 figure
Low-complexity 8-point DCT Approximation Based on Angle Similarity for Image and Video Coding
The principal component analysis (PCA) is widely used for data decorrelation
and dimensionality reduction. However, the use of PCA may be impractical in
real-time applications, or in situations were energy and computing constraints
are severe. In this context, the discrete cosine transform (DCT) becomes a
low-cost alternative to data decorrelation. This paper presents a method to
derive computationally efficient approximations to the DCT. The proposed method
aims at the minimization of the angle between the rows of the exact DCT matrix
and the rows of the approximated transformation matrix. The resulting
transformations matrices are orthogonal and have extremely low arithmetic
complexity. Considering popular performance measures, one of the proposed
transformation matrices outperforms the best competitors in both matrix error
and coding capabilities. Practical applications in image and video coding
demonstrate the relevance of the proposed transformation. In fact, we show that
the proposed approximate DCT can outperform the exact DCT for image encoding
under certain compression ratios. The proposed transform and its direct
competitors are also physically realized as digital prototype circuits using
FPGA technology.Comment: 16 pages, 12 figures, 10 table
Low-complexity 8-point DCT Approximations Based on Integer Functions
In this paper, we propose a collection of approximations for the 8-point
discrete cosine transform (DCT) based on integer functions. Approximations
could be systematically obtained and several existing approximations were
identified as particular cases. Obtained approximations were compared with the
DCT and assessed in the context of JPEG-like image compression.Comment: 21 pages, 4 figures, corrected typo
Fast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity
We propose an approximation method for thresholding of singular values using
Chebyshev polynomial approximation (CPA). Many signal processing problems
require iterative application of singular value decomposition (SVD) for
minimizing the rank of a given data matrix with other cost functions and/or
constraints, which is called matrix rank minimization. In matrix rank
minimization, singular values of a matrix are shrunk by hard-thresholding,
soft-thresholding, or weighted soft-thresholding. However, the computational
cost of SVD is generally too expensive to handle high dimensional signals such
as images; hence, in this case, matrix rank minimization requires enormous
computation time. In this paper, we leverage CPA to (approximately) manipulate
singular values without computing singular values and vectors. The thresholding
of singular values is expressed by a multiplication of certain matrices, which
is derived from a characteristic of CPA. The multiplication is also efficiently
computed using the sparsity of signals. As a result, the computational cost is
significantly reduced. Experimental results suggest the effectiveness of our
method through several image processing applications based on matrix rank
minimization with nuclear norm relaxation in terms of computation time and
approximation precision.Comment: This is a journal pape
A Discrete Tchebichef Transform Approximation for Image and Video Coding
In this paper, we introduce a low-complexity approximation for the discrete
Tchebichef transform (DTT). The proposed forward and inverse transforms are
multiplication-free and require a reduced number of additions and bit-shifting
operations. Numerical compression simulations demonstrate the efficiency of the
proposed transform for image and video coding. Furthermore, Xilinx Virtex-6
FPGA based hardware realization shows 44.9% reduction in dynamic power
consumption and 64.7% lower area when compared to the literature.Comment: 13 pages, 5 figures, 2 table
Multi-Beam RF Aperture Using Multiplierless FFT Approximation
Multiple independent radio frequency (RF) beams find applications in
communications, radio astronomy, radar, and microwave imaging. An -point FFT
applied spatially across an array of receiver antennas provides -independent
RF beams at multiplier complexity. Here, a low-complexity
multiplierless approximation for the 8-point FFT is presented for RF
beamforming, using only 26 additions. The algorithm provides eight beams that
closely resemble the antenna array patterns of the traditional FFT-based
beamformer albeit without using multipliers. The proposed FFT-like algorithm is
useful for low-power RF multi-beam receivers; being synthesized in 45 nm CMOS
technology at 1.1 V supply, and verified on-chip using a Xilinx Virtex-6 Lx240T
FPGA device. The CMOS simulation and FPGA implementation indicate bandwidths of
588 MHz and 369 MHz, respectively, for each of the independent receive-mode RF
beams.Comment: 8 pages, 3 figures, 2 tables, sfg correcte
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