Journal ArticleDOI
New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
TLDR
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise C2 edges.Abstract:
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along piecewise C 2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle-shaped elements at fine scales. These elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets. For instance, curvelets obey a parabolic scaling relation which says that at scale 2 -j , each element has an envelope that is aligned along a ridge of length 2 -j/2 and width 2 -j . We prove that curvelets provide an essentially optimal representation of typical objects f that are C 2 except for discontinuities along piecewise C 2 curves. Such representations are nearly as sparse as if f were not singular and turn out to be far more sparse than the wavelet decomposition of the object. For instance, the n-term partial reconstruction f C n obtained by selecting the n largest terms in the curvelet series obeys ∥f - f C n ∥ 2 L2 ≤ C . n -2 . (log n) 3 , n → ∞. This rate of convergence holds uniformly over a class of functions that are C 2 except for discontinuities along piecewise C 2 curves and is essentially optimal. In comparison, the squared error of n-term wavelet approximations only converges as n -1 as n → ∞, which is considerably worse than the optimal behavior.read more
Citations
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Journal ArticleDOI
On the stable sampling rate for binary measurements and wavelet reconstruction
TL;DR: It is shown that for binary measurements (modelled with Walsh functions and Hadamard matrices) and wavelet reconstruction the stable sampling rate is linear, implying that binary measurements are as efficient as Fourier samples when using wavelets as the reconstruction space.
Journal ArticleDOI
Secure transmission and integrity verification of color radiological images using fast discrete curvelet transform and compressive sensing
TL;DR: The Compressive Sensing (CS) theory is used to encrypt the color secret image before embedding them into high frequency Fast Discrete Curvelet Transform (FDCuT) coefficients of color radiological images, which demonstrates better performance in terms of imperceptibility of stego color Radiological image.
Journal Article
Comparison of wavelet, Gabor and curvelet transform for face recognition
TL;DR: This paper makes a systematic comparison of wavelet, Gabor and curvelet for recognition, and finds the best subband irrelevant to expression and illumination changes, and combines the multiscale analysis with subspace decomposition as the algorithm.
Proceedings ArticleDOI
Robust digital image watermarking in curvelet domain
TL;DR: The proposed scheme provides an accurate estimation of single and/or combined geometrical distortions and is relied on edge detection and radon transform and the fidelity of the protected image is well maintained.
Journal ArticleDOI
A Robust Actin Filaments Image Analysis Framework.
Mitchel Alioscha-Perez,Carine Benadiba,Katty Goossens,Katty Goossens,Sandor Kasas,Giovanni Dietler,Ronnie Willaert,Ronnie Willaert,Hichem Sahli,Hichem Sahli,Hichem Sahli +10 more
TL;DR: The proposed robust actin filaments image analysis framework allows extracting individual filaments in the presence of noise, artifacts and heavy blurring and provides numerous parameters such as filaments orientation, position and length, useful for further analysis.
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