2,478 research outputs found
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
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
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
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
The discrete fractional random cosine and sine transforms
Based on the discrete fractional random transform (DFRNT), we present the
discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We
demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of
DFRNT and thus their mathematical properties are inherited from the DFRNT.
Numeral results of DFRNCT and DFRNST for one and two dimensional functions have
been given.Comment: 15 pages, 4 eps figures. LaTe
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
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
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
Signal Flow Graph Approach to Efficient DST I-IV Algorithms
In this paper, fast and efficient discrete sine transformation (DST)
algorithms are presented based on the factorization of sparse, scaled
orthogonal, rotation, rotation-reflection, and butterfly matrices. These
algorithms are completely recursive and solely based on DST I-IV. The presented
algorithms have low arithmetic cost compared to the known fast DST algorithms.
Furthermore, the language of signal flow graph representation of digital
structures is used to describe these efficient and recursive DST algorithms
having points signal flow graph for DST-I and points signal flow
graphs for DST II-IV
ACDC: A Structured Efficient Linear Layer
The linear layer is one of the most pervasive modules in deep learning
representations. However, it requires parameters and
operations. These costs can be prohibitive in mobile applications or prevent
scaling in many domains. Here, we introduce a deep, differentiable,
fully-connected neural network module composed of diagonal matrices of
parameters, and , and the discrete cosine transform
. The core module, structured as , has
parameters and incurs operations. We present theoretical results
showing how deep cascades of ACDC layers approximate linear layers. ACDC is,
however, a stand-alone module and can be used in combination with any other
types of module. In our experiments, we show that it can indeed be successfully
interleaved with ReLU modules in convolutional neural networks for image
recognition. Our experiments also study critical factors in the training of
these structured modules, including initialization and depth. Finally, this
paper also provides a connection between structured linear transforms used in
deep learning and the field of Fourier optics, illustrating how ACDC could in
principle be implemented with lenses and diffractive elements
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