The Experts below are selected from a list of 84435 Experts worldwide ranked by ideXlab platform
Wenjing Liao - One of the best experts on this subject based on the ideXlab platform.
-
stable super resolution limit and smallest Singular Value of restricted fourier matrices
Applied and Computational Harmonic Analysis, 2021Co-Authors: Wenjing LiaoAbstract:Abstract We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given M + 1 of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable recovery when the distance Δ between the two closest point sources is less than 1 / M . We introduce a clumps model where the point sources are closely spaced within several clumps. Under this assumption, we derive a non-asymptotic lower bound for the minimum Singular Value of a Vandermonde matrix whose nodes are determined by the point sources. Our estimate is given as a weighted l 2 sum, where each term only depends on the configuration of each individual clump. The main novelty is that our lower bound obtains an exact dependence on the Super-Resolution Factor S R F = ( M Δ ) − 1 . As noise level increases, the sensitivity of the noise-space correlation function in the MUSIC algorithm degrades according to a power law in SRF where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum Singular Value and the sensitivity of MUSIC. We also provide lower and upper bounds for a min-max error of super-resolution for the grid model, which in turn is closely related to the minimum Singular Value of Vandermonde matrices.
-
stable super resolution limit and smallest Singular Value of restricted fourier matrices
arXiv: Information Theory, 2017Co-Authors: Wenjing LiaoAbstract:We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given $M$ of its noisy low-frequency Fourier coefficients. Super-resolution refers to a stable recovery when the distance $\Delta$ between the two closest point sources is less than $1/M$. We introduce a clumps model where the point sources are closely spaced within several clumps. Under this assumption, we derive a non-asymptotic lower bound for the minimum Singular Value of a Vandermonde matrix whose nodes are determined by the point sources. Our estimate is given as a weighted $\ell^2$ sum, where each term only depends on the configuration of each individual clump. The main novelty is that our lower bound obtains an exact dependence on the {\it Super-Resolution Factor} $SRF=(M\Delta)^{-1}$. As noise level increases, the {\it sensitivity of the noise-space correlation function in the MUSIC algorithm} degrades according to a power law in $SRF$ where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum Singular Value and the sensitivity of MUSIC. We also provide lower and upper bounds for a min-max error of super-resolution for the grid model, which in turn is closely related to the minimum Singular Value of Vandermonde matrices.
Gholamreza Anbarjafari - One of the best experts on this subject based on the ideXlab platform.
-
satellite image contrast enhancement using discrete wavelet transform and Singular Value decomposition
IEEE Geoscience and Remote Sensing Letters, 2010Co-Authors: Hasan Demirel, Cagri Ozcinar, Gholamreza AnbarjafariAbstract:In this letter, a new satellite image contrast enhancement technique based on the discrete wavelet transform (DWT) and Singular Value decomposition has been proposed. The technique decomposes the input image into the four frequency subbands by using DWT and estimates the Singular Value matrix of the low-low subband image, and, then, it reconstructs the enhanced image by applying inverse DWT. The technique is compared with conventional image equalization techniques such as standard general histogram equalization and local histogram equalization, as well as state-of-the-art techniques such as brightness preserving dynamic histogram equalization and Singular Value equalization. The experimental results show the superiority of the proposed method over conventional and state-of-the-art techniques.
-
image equalization based on Singular Value decomposition
International Symposium on Computer and Information Sciences, 2008Co-Authors: Hasan Demirel, Gholamreza Anbarjafari, Mohammad N S JahromiAbstract:In this paper, a novel image equalization technique which is based on Singular Value decomposition (SVD) is proposed. The Singular Value matrix represents the intensity information of the given image and any change on the Singular Values change the intensity of the input image. The proposed technique converts the image into the SVD domain and after normalizing the Singular Value matrix it reconstructs the image in the spatial domain by using the updated Singular Value matrix. The technique is called the Singular Value equalization (SVE) and compared with the standard grayscale histogram equalization (GHE) method. The visual and quantitative results suggest that the proposed SVE method clearly outperforms the GHE method.
Hasan Demirel - One of the best experts on this subject based on the ideXlab platform.
-
satellite image contrast enhancement using discrete wavelet transform and Singular Value decomposition
IEEE Geoscience and Remote Sensing Letters, 2010Co-Authors: Hasan Demirel, Cagri Ozcinar, Gholamreza AnbarjafariAbstract:In this letter, a new satellite image contrast enhancement technique based on the discrete wavelet transform (DWT) and Singular Value decomposition has been proposed. The technique decomposes the input image into the four frequency subbands by using DWT and estimates the Singular Value matrix of the low-low subband image, and, then, it reconstructs the enhanced image by applying inverse DWT. The technique is compared with conventional image equalization techniques such as standard general histogram equalization and local histogram equalization, as well as state-of-the-art techniques such as brightness preserving dynamic histogram equalization and Singular Value equalization. The experimental results show the superiority of the proposed method over conventional and state-of-the-art techniques.
-
image equalization based on Singular Value decomposition
International Symposium on Computer and Information Sciences, 2008Co-Authors: Hasan Demirel, Gholamreza Anbarjafari, Mohammad N S JahromiAbstract:In this paper, a novel image equalization technique which is based on Singular Value decomposition (SVD) is proposed. The Singular Value matrix represents the intensity information of the given image and any change on the Singular Values change the intensity of the input image. The proposed technique converts the image into the SVD domain and after normalizing the Singular Value matrix it reconstructs the image in the spatial domain by using the updated Singular Value matrix. The technique is called the Singular Value equalization (SVE) and compared with the standard grayscale histogram equalization (GHE) method. The visual and quantitative results suggest that the proposed SVE method clearly outperforms the GHE method.
Jacquelien M.a. Scherpen - One of the best experts on this subject based on the ideXlab platform.
-
hankel Singular Value functions from schmidt pairs for nonlinear input output systems
Systems & Control Letters, 2005Co-Authors: Steven W Gray, Jacquelien M.a. ScherpenAbstract:This paper presents three results in Singular Value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel Singular Value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known to exist then a set of sufficient conditions is given for the existence of a Schmidt pair, and the state space provides a convenient representation of the corresponding Singular Value function. Finally, it is shown that in a specific coordinate frame it is possible to relate this new Singular Value function definition to the original state space notion used to describe nonlinear balanced realizations.
-
Singular Value analysis of hankel operators for general nonlinear systems
European Control Conference, 2003Co-Authors: Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:This paper discusses Singular Value analysis of Hankel operators for both continuous-time and discrete-time general nonlinear systems. Singular Value analysis clarifies the gain structure of a given operator. Here it is proven that Singular Value analysis of smooth Hankel operators defined on Hilbert spaces can be characterized by simple equations in terms of their states. A balancing and model reduction procedure is derived based on it. In particular, when the proposed model reduction method is applied to continuous-time nonlinear systems, several gain properties such as Hankel norm, controllability and observability functions are preserved.
-
on the nonuniqueness of Singular Value functions and balanced nonlinear realizations
Systems & Control Letters, 2001Co-Authors: Steven W Gray, Jacquelien M.a. ScherpenAbstract:The notion of balanced realizations for nonlinear state space model reduction was first introduced in 1993. Analogous to the linear case, the so called Singular Value functions of a system describe the relative importance of each state component from an input-output point of view. In this paper it is shown that the usual procedure for nonlinear balancing has some interesting ambiguities that do not occur in the linear case. Specifically, it appears that the Singular Value functions as currently defined are dependent on a particular factorization of the observability function. It is shown by example that in a fixed coordinate frame this factorization is not unique, and thus other distinct definitions for the Singular Value functions and balanced realizations are possible. One method relating Singular Value functions from different factorizations is presented.
Paul Bao - One of the best experts on this subject based on the ideXlab platform.
-
Image adaptive watermarking using wavelet domain Singular Value decomposition
IEEE Transactions on Circuits and Systems for Video Technology, 2005Co-Authors: Paul BaoAbstract:In this letter, we propose a novel, yet simple, image-adaptive watermarking scheme for image authentication by applying a simple quantization-index-modulation process on wavelet domain Singular Value decomposition. Unlike the traditional wavelet-based watermarking schemes where the watermark bits are embedded directly on the wavelet coefficients, the proposed scheme is based on bit embedding on the Singular Value (luminance) of the blocks within wavelet subband of the original image. To improve the fidelity and the perceptual quality of the watermarked image and to enhance the security of watermarking, we model the adaptive quantization parameters based on the statistics of blocks within subbands. The scheme is robust against JPEG compression but extremely sensitive to malicious manipulation such as filtering and random noising. Watermark detection is efficient and blind in the sense only the quantization parameters but not the original image are required. The quantization parameters adaptive to blocks are vector quantized to reduce the watermarking overhead.
