Scientists / Open questions

斯特凡·马拉

Stéphane Mallat

小波分析、信号处理、机器学习

10 个问题

Completeness, stability, and provably accurate reconstruction for the wavelet transform modulus maxima representation of signals and images
Stability, wavelet-basis dependence, and nonlinear time-scaling of space–time adaptive wavelet schemes for time-dependent PDEs (the open questions of Bacry–Mallat–Papanicolaou, 1992)
Bandelet surface compression: closing the theory-practice gap between the Alpert-based approximation theorem and the implemented wavelet transform, and controlling geometric rather than L2 distortion
Completing a rigorous distortion-rate theory for low-bit-rate transform coding of natural images: stochastic image models, optimized bases, and analytic coding-overhead bounds
Statistical decision theory for the adaptive best-basis covariance estimator of locally stationary processes
Theoretical recovery guarantees for Gaussian-mixture-model piecewise-linear estimation in linear inverse problems and compressed sensing
Completeness, stability, and wavelet-class characterization for the stabilized dyadic zero-crossing representation (Mallat, 1991)
Statistical guarantees for Stein-risk-driven adaptive block thresholding in redundant time-frequency frames under nonstationary noise
Completing the statistical foundations of shape from texture via the Texture Gradient Equation: homogeneity characterization, two-dimensional consistency, identifiability, and non-Lambertian texture models
Recovery and stability guarantees for blockwise sparse mixing estimators (SME) and their greedy OBMP solver

返回开放问题

Completeness, stability, and provably accurate reconstruction for the wavelet transform modulus maxima representation of signals and images

Stability, wavelet-basis dependence, and nonlinear time-scaling of space–time adaptive wavelet schemes for time-dependent PDEs (the open questions of Bacry–Mallat–Papanicolaou, 1992)

Bandelet surface compression: closing the theory-practice gap between the Alpert-based approximation theorem and the implemented wavelet transform, and controlling geometric rather than L2 distortion

Completing a rigorous distortion-rate theory for low-bit-rate transform coding of natural images: stochastic image models, optimized bases, and analytic coding-overhead bounds

Statistical decision theory for the adaptive best-basis covariance estimator of locally stationary processes

Theoretical recovery guarantees for Gaussian-mixture-model piecewise-linear estimation in linear inverse problems and compressed sensing

Completeness, stability, and wavelet-class characterization for the stabilized dyadic zero-crossing representation (Mallat, 1991)

Statistical guarantees for Stein-risk-driven adaptive block thresholding in redundant time-frequency frames under nonstationary noise

Completing the statistical foundations of shape from texture via the Texture Gradient Equation: homogeneity characterization, two-dimensional consistency, identifiability, and non-Lambertian texture models

Recovery and stability guarantees for blockwise sparse mixing estimators (SME) and their greedy OBMP solver