Inspired by the great success of deep neural networks (DNNs), many unfolding methods
have been proposed to integrate traditional image modeling techniques, such as dictionary …

The richness of natural images makes the quest for optimal representations in image
processing and computer vision challenging. The latter observation has not prevented the …

This paper describes two digital implementations of a new mathematical transform, namely,
the second generation curvelet transform in two and three dimensions. The first digital …

The paper discusses the theory behind the dual-tree transform, shows how complex
wavelets with good properties can be designed, and illustrates a range of applications in …

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 …

Historically, the theory of Hilbert spaces originated from David Hilbert's (1862–1943) work
on quadratic forms in infinitely many variables with their applications to integral equations …

This book presents the state of the art in sparse and multiscale image and signal processing,
covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and …

The contourlet transform is a new two-dimensional extension of the wavelet transform using
multiscale and directional filter banks. The contourlet expansion is composed of basis …

We propose a new scheme, named contourlet, that provides a flexible multiresolution, local
and directional image expansion. The contourlet transform is realized efficiently via a double …

This paper introduces a new class of bases, called bandelet bases, which decompose the
image along multiscale vectors that are elongated in the direction of a geometric flow. This …