Showing papers on "Hadamard transform published in 2010"
TL;DR: In this paper, some inequalities of Hadamard's type for quasi-convex functions are given and some error estimates for the Trapezoidal formula are obtained.
Abstract: In this paper, some inequalities of Hadamard's type for quasi-convex functions are given. Some error estimates for the Trapezoidal formula are obtained. Applications to some special means are considered.
116 citations
TL;DR: Some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m -convex are given.
108 citations
TL;DR: This paper shows how frequency-dependent Hadamard ratios must be merged into a single test statistic when the vectors-valued random variable is replaced by a vector-valued time series with temporal correlation.
Abstract: This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. For wide sense stationary (WSS) Gaussian processes, this is a problem of deciding between two different power spectral density matrices, one of them diagonal. Specifically, we show that for arbitrary Gaussian processes (not necessarily WSS) the generalized likelihood ratio test (GLRT) is given by the quotient between the determinant of the sample space-time covariance matrix and the determinant of its block-diagonal version. Furthermore, for WSS processes, we present an asymptotic frequency-domain approximation of the GLRT which is given by a function of the Hadamard ratio (quotient between the determinant of a matrix and the product of the elements of the main diagonal) of the estimated power spectral density matrix. The Hadamard ratio is known to be the GLRT detector for vector-valued random variables and, therefore, what this paper shows is how frequency-dependent Hadamard ratios must be merged into a single test statistic when the vector-valued random variable is replaced by a vector-valued time series with temporal correlation. For bivariate time series, the derived frequency domain detector can be rewritten as a function of the well-known magnitude squared coherence (MSC) spectrum, which suggests a straightforward extension of the MSC spectrum to the general case of multivariate time series. Finally, the performance of the proposed method is illustrated by means of simulations.
107 citations
Posted Content•
TL;DR: In this article, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given, and some error estimates for the trapezoidal formula are obtained.
Abstract: In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are obtained.
89 citations
TL;DR: In this article, the wave equation with supercritical interior and boundary sources and damping terms is considered and local Hadamard well-posedness of finite energy solutions is obtained.
85 citations
TL;DR: The computational requirement of the proposed algorithm is about 1.5 additions per projection vector per sample, which is the lowest among existing fast algorithms for Walsh Hadamard Transform on sliding windows.
Abstract: This paper proposes a fast algorithm for Walsh Hadamard Transform on sliding windows which can be used to implement pattern matching most efficiently. The computational requirement of the proposed algorithm is about 1.5 additions per projection vector per sample, which is the lowest among existing fast algorithms for Walsh Hadamard Transform on sliding windows.
76 citations
TL;DR: For functions whose second derivatives absolute values are quasi-convex, this paper obtained some inequalities of Hermite-Hadamard type for functions with absolute values in the form of
Abstract: In this note we obtain some inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex. Applications for special means are also provided.
62 citations
TL;DR: In this article, two iterative algorithms for nonexpansive mappings on Hadamard manifolds, which are extensions of the well-known Halpern's and Mann's algorithms in Euclidean spaces, are proposed and proved to be convergent to a fixed point of the mapping.
Abstract: Two iterative algorithms for nonexpansive mappings on Hadamard manifolds, which are extensions of the well-known Halpern\'s and Mann\'s algorithms in Euclidean spaces, are proposed and proved to be convergent to a fixed point of the mapping. Some numerical examples are provided.
58 citations
TL;DR: In this article, local convergence analysis of the proximal point method for a special class of nonconvex functions on Hadamard manifold is presented, and it is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.
Abstract: Local convergence analysis of the proximal point method for a special class of nonconvex functions on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.
57 citations
16 Aug 2010
TL;DR: An orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform is proposed and an efficient algorithm for its fast computation is developed.
Abstract: In this paper, we propose an orthogonal multiplication-free transform of order that is an integral power of two by an appropriate extension of the well-known fourthorder integer discrete cosine transform. Moreover, we develop an efficient algorithm for its fast computation. It is shown that the computational and structural complexities of the algorithm are similar to that of the Hadamard transform. By applying the proposed transform to image compression, we show that it outperforms the existing transforms having complexities similar to that of the proposed one.
57 citations
TL;DR: The usage of Hadamard transform as signal decomposition tool offers advantages in terms of simpler implementation, low computation cost and high resiliency at low quality compression considering both JPEG and JPEG 2000 framework.
Abstract: The paper proposes a digital image watermarking scheme that selects regions for data embedding based on information measure. Two valued kernels of Hadamard transformation cause smaller image information change during embedding compared to other transform domains such as DCT (discrete cosine transform), DFT (discrete Fourier transform), Fourier–Mellin and wavelet-based embedding. Moreover, the usage of Hadamard transform as signal decomposition tool offers advantages in terms of simpler implementation, low computation cost and high resiliency at low quality compression considering both JPEG and JPEG 2000 framework. Compression resiliency is further improved using adaptive negative modulation. These facts are validated comparing the performance with some other existing watermarking schemes as well as DCT domain implementation of the proposed scheme.
TL;DR: For log-convex functions, this article gave the extensions of the results given by Gill et al. (1997) and obtained some new Hadamard-type inequalities.
Abstract: We do not only give the extensions of the results given by Gill et al. (1997) for log-convex functions but also obtain some new Hadamard-type inequalities for log-convex -convex, and -convex functions.
TL;DR: In this article, a new scheme for controlled teleportation of an arbitrary two-particle pure or mixed state with the help of a five-qubit cluster state is proposed in detail.
Abstract: A new scheme for controlled teleportation of an arbitrary two-particle pure or mixed state with the help of a five-qubit cluster state is proposed in detail. In this scheme, a five-particle cluster state is shared by a sender, a controller and a receiver. At first, the sender performs a four-qubit von-Neumann measurement on the qubits at hand, and the controller performs a Hadamard measurement on his qubit. Then the receiver can reconstruct the arbitrary two-particle pure or mixed state by performing some appropriate unitary transformations on his particles after he knows the measure results of the sender and the controller. This controlled teleportation scheme is deterministic.
TL;DR: A novel compression scheme with a tunable complexity-rate-distortion trade-off that intends to perform better than the CCSDS standard while preserving low complexity and easy rate control is proposed.
Book•
20 Oct 2010
TL;DR: Low level algorithms as mentioned in this paper use bit wizardry and permutations and their operations to find paths in directed graphs and search paths for directed graphs in directed graph graphs, using the GP language.
Abstract: Low level algorithms.- Bit wizardry.- Permutations and their operations.- Sorting and searching.- Data structures.- Combinatorial generation.- Conventions and considerations.- Combinations.- Compositions.- Subsets.- Mixed radix numbers.- Permutations.- Multisets.- Gray codes for string with restrictions.- Parenthesis strings.- Integer partitions.- Set partitions.- Necklaces and Lyndon words.- Hadamard and conference matrices.- Searching paths in directed graphs.- Fast transforms.- The Fourier transform.- Convolution, correlation, and more FFT algorithms.- The Walsh transform and its relatives.- The Haar transform.- The Hartley transform.- Number theoretic transforms (NTTs).- Fast wavelet transforms.- Fast arithmetic.- Fast multiplication and exponentiation.- Root extraction.- Iterations for the inversion of a function.- The AGM, elliptic integrals, and algorithms for computing.- Logarithm and exponential function.- Computing the elementary functions with limited resources.- Numerical evaluation of power series.- Cyclotomic polynomials, product forms, and continued fractions.- Synthetic Iterations.-. Algorithms for finite fields.- Modular arithmetic and some number theory.- Binary polynomials.- Shift registers.- Binary finite fields.- The electronic version of the book.- Machine used for benchmarking.- The GP language.- Bibliography.- Index.
TL;DR: An “Illumination Watermarking” technology with which the images of objects without copyright protection can contain invisible digital watermarking is proposed, and embedded data could be read out with almost 100% accuracy in both cases.
Abstract: We have proposed an “Illumination Watermarking” technology with which the images of objects without copyright protection can contain invisible digital watermarking. This technology uses spatially modulated illumination possibly using an orthogonal transform, such as discrete cosine transform (DCT), as the method of embedding watermarks, and it can be applied to objects that do not have electronically embedded watermarking such as pictures painted by artists. We conducted a new series of experiments where one-bit binary data were embedded in one block that consisted of 8 × 8 pixels using the phase of the highest frequency component generated by a Walsh-Hadamard transform (WHT) as well as DCT. The experimental results revealed that embedded data could be read out with almost 100% accuracy in both cases, where the embedded watermarked image could hardly be observed. We also found that the influence of JPEG compression, which is commonly used in digital cameras, was very small.
01 Jan 2010
TL;DR: From the average precision and average recall values obtained by firing 55 queries on the image database it is found that use of row mean and column mean with image fragmentation improves the performance resulting in better image retrieval.
Abstract: Always the thrust for better and faster image retrieval techniques has nourished the research in content based image retrieval. The paper presents 32 novel image retrieval techniques using the feature vectors obtained by applying Walsh transform on row mean and column mean of full image, four fragments, sixteen fragments and 64 fragments of image. All the proposed CBIR techniques are tested on generic image database of size 1000 with 11 image classes. From the average precision and average recall values obtained by firing 55 queries on the image database it is found that use of row mean and column mean with image fragmentation improves the performance resulting in better image retrieval. In all these techniques to speed up the image retrieval process notion of energy compaction is introduced and tested for 100%, 95%, 90% and 85% of energy of feature vectors using Walsh transform.
TL;DR: In this paper, the equivalence classes of Hadamard matrices of order at most 28 have been found by 1994, and the remaining two types of these matrices are expected to be insigniflcant.
Abstract: All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We flnd all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another type. Based on experience with the classiflcation of Hadamard matrices of smaller order, it is expected that the number of the remaining two types of these matrices, relative to the total number of Hadamard matrices of order 32, to be insigniflcant.
TL;DR: This paper presents a high-throughput, cost-effective implementation of six different integer transforms in the H.264/AVC high-profile coders, i.e., 4 × 4 forward,4 × 4 inverse, forward Hadamard, inverse Hadamards, 8 × 8 forward, and 8 ×8 inverse transform, all integrated as a shared hardware.
Abstract: This paper presents a high-throughput, cost-effective implementation of six different integer transforms in the H.264/AVC high-profile coders, i.e., 4 × 4 forward, 4 × 4 inverse, forward Hadamard, inverse Hadamard, 8 × 8 forward, and 8 × 8 inverse transform, all integrated as a shared hardware. The 4 × 4 transform matrices are regularized by using permutation, partitioned into 2 × 2 blocks, and factored for maximal hardware sharing. By using two types of 4 × 4 transform matrices included in an 8 × 8 transform matrix, two different 8 × 8 transforms are both described as three steps and unified with minor modification. To improve throughput of the transform, two independent 4 × 4 transform blocks within the 8 × 8 transform block operate in parallel in the 4 × 4 transform mode, while the two-stage pipelined architecture is used in the 8 × 8 transform mode. Using 0.18-?m CMOS technology, the maximum operating frequency of the proposed multitransform architecture is 200 MHz, which achieves 4.1 Gpixels/sec throughput rate with the hardware cost of 63618 gates. Compared with existing designs, the proposed design delivers at least 54% higher throughput at 38% higher throughput/area ratio in Adaptive Block-size Transform (ABT) mode.
TL;DR: The existence of partial Hadamard matrices can be proved by showing that there is positive probability of a random walk returning to the origin after a specified number of steps, and the number of these designs can be approximated by estimating the return probabilities.
Abstract: In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and equivalence classes of partial Hadamard matrices. Therefore, the existence of partial Hadamard matrices can be proved by showing that there is positive probability of a random walk returning to the origin after a specified number of steps. Moreover, the number of these designs can be approximated by estimating the return probabilities. We use the inversion formula for the Fourier transform of the random walk to provide such estimates. We also include here an upper bound, derived by elementary methods, on the number of partial Hadamard matrices.
29 Aug 2010
TL;DR: The Hadamard transform has been adopted which requires less computation time than the commonly used DCT, and a refinement step exploitsspatial continuity constraints along the patch borders toprevent erroneous patch selections.
Abstract: In this paper, we present a new and fast techniquefor background estimation from cluttered image sequences.Most of the background initialization approaches developedso far collect a number of initial frames and then requirea slow estimation step which introduces a delay wheneverit is applied. Conversely, the proposed technique redistributesthe computational load among all the frames bymeans of a patch by patch preprocessing, which makesthe overall algorithm more suitable for real-time applications.For each patch location a prototype set is created andmaintained. The background is then iteratively estimatedby choosing from each set the most appropriate candidatepatch, which should verify a sort of frequency coherencewith its neighbors. To this aim, the Hadamard transformhas been adopted which requires less computation time thanthe commonly used DCT. Finally, a refinement step exploitsspatial continuity constraints along the patch borders toprevent erroneous patch selections. The approach has beencompared with the state of the art on videos from availabledatasets (ViSOR and CAVIAR), showing a speed up of about10 times and an improved accuracy.
13 Jun 2010
TL;DR: Wang et al. as discussed by the authors proposed to use the orthogonal Haar transform (OHT) for pattern matching, the algorithm using strip sum requires O(log u) additions per pixel to project input data of size N × N onto u 2-D OHT basis.
Abstract: Pattern matching is a widely used procedure in signal processing, computer vision, image and video processing. Recently, methods using Walsh Hadamard Transform (WHT) and Gray-Code kernels (GCK) are successfully applied for fast transform domain pattern matching. This paper introduces strip sum on the image. The sum of pixels in a rectangle can be computed by one addition using the strip sum. Then we propose to use the orthogonal Haar transform (OHT) for pattern matching. Applied for pattern matching, the algorithm using strip sum requires O(log u) additions per pixel to project input data of size N × N onto u 2-D OHT basis while existing fast algorithms require O(u) additions per pixel to project the same data onto u 2-D WHT or GCK basis. Experimental results show the efficiency of pattern matching using OHT.
03 Dec 2010
TL;DR: For functions whose derivatives absolute values are m-convex, this paper established several inequalities of Hermite Hadamard type for functions with absolute values that are m −convariant.
Abstract: In this paper, we establish several inequalities of Hermite‐Hadamard type for functions whose derivatives absolute values are m‐convex.
TL;DR: In this article, the Hermite-Hadamard integral inequalities for differantiable mappings of real numbers are established. But these inequalities are not applicable to the case of real-valued mappings.
Abstract: In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
26 Feb 2010
TL;DR: The new technique for image retrieval using the color-texture features extracted from images based on vector quantization with Kekre's fast codebook generation is proposed, which gives better discrimination capability for CBIR.
Abstract: The new technique for image retrieval using the color-texture features extracted from images based on vector quantization with Kekre's fast codebook generation is proposed. This gives better discrimination capability for CBIR. Here the database image is divided into 2x2 pixel windows to obtain 12 color descriptors per window (Red, Green and Blue per pixel) to form a vector. Collection of all such vectors is a training set. Then the Kekre's Fast Codebook Generation (KFCG) is applied on this set to get 16 codevectors. The Walsh transform is applied on each column of the codebook, followed by Kekre's transform applied on each row of the Walsh transformed codebook. This transform vector then is used as the image signature (feature vector) for image retrieval. The method takes lesser computations as compared to conventional Walsh applied on complete image. The method gives the color-texture features of the image database at reduced feature set size. Proposed method gives better precision and recall as compared to full Walsh based CBIR. Proposed method avoids resizing of images which is required for any transform based feature extraction method.
TL;DR: Advances in 20 specific problems and several new research directions are outlined, especially cocyclic Hadamard matrices, their generalisations and applications, made over the past three years.
Abstract: We survey research progress in Hadamard matrices, especially cocyclic Hadamard matrices, their generalisations and applications, made over the past three years. Advances in 20 specific problems and several new research directions are outlined. Two new problems are presented.
TL;DR: A generalized framework for DFT called Generalized DFT (GDFT) with nonlinear phase by exploiting the phase space is presented, showing that GDFT offers sizable correlation improvements over DFT, Walsh, Oppermann and Gold codes, leading to better performance in all multi-carrier communications scenarios investigated.
Abstract: Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. In this paper, we present a generalized framework for DFT called Generalized DFT (GDFT) with nonlinear phase by exploiting the phase space. We show that GDFT offers sizable correlation improvements over DFT, Walsh, Oppermann and Gold codes, leading to better performance in all multi-carrier communications scenarios investigated. We also highlight how known constant modulus orthogonal transforms are special solutions of the proposed GDFT framework. Moreover, we introduce practical design methods offering computationally efficient implementations of GDFT as enhancements to DFT. We conclude the paper with examples of communications applications where GDFT is shown to outperform DFT and other known constant modulus bases.
Posted Content•
TL;DR: In this paper, the authors constructed exponentionally many non-isomorphic skew Hadamard difference sets over an elementary abelian group of order $q^3.
Abstract: In this paper we construct exponentionally many non-isomorphic skew Hadamard difference sets over an elementary abelian group of order $q^3$.
30 Sep 2010
TL;DR: The importance of security of BE systems in relation to an Error Correcting Code (ECC) is emphasized and it is shown that the error correcting scheme with zero insertions can be easily cracked by an attacker.
Abstract: The importance of security of BE systems in relation to an Error Correcting Code (ECC) is emphasized. The security of the BE system proposed in Kanade et al paper “Three Factor Scheme For Biometric-Based Cryptographic Key Regeneration Using Iris” is analyzed. It is shown that the error correcting scheme with zero insertions, which was employed in the paper, can be easily cracked by an attacker. By knowing the locations of only 7 zeros for each 32-bit block of the Hadamard ECC, an attacker can reconstruct the entire 198-bit key within a fraction of a second. The generalization of the attack for the ECCs other than Hadamard is discussed.
03 May 2010
TL;DR: An energy-efficient method for data transmission through improved data compression, based on the Walsh transform, that enables significant saving in the energy expenditure during wireless signal transmission is presented.
Abstract: This paper presents an energy-efficient method for data transmission through improved data compression. This is achieved by a new signal source coding method based on the Walsh transform. This research is motivated by the need for extended service life of wireless sensor networks, where individual sensor nodes are energy constrained. Theoretical background is introduced, and its effectiveness is established through simulations and experiments. The simulations are conducted using electrocardiogram (ECG) and bearing vibration signals, and the results are comparatively evaluated against the Haar transform coding, discrete cosine transform (DCT) coding, pulse code modulation, and fixed-word-length Walsh coding. Experimental verification is performed by implementing the algorithm on a wireless test bed. Results indicate that up to 58% energy reduction can be achieved for wireless transmission of ECG signals, as compared to other commonly used coding methods. For bearing vibration signal transmission, the energy consumed during transmission is comparable to that of the near-optimal DCT coding.