Framing pyramids

By Minh N. Do, Martin Vetterli. IEEE Transactions on Signal Processing, 2003

315 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/e3207926ad8213a452c5ab0e99cde0d0066509c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

An Efficient Pan-Sharpening Method via a Combined Adaptive PCA Approach and Contourlets (2008, background): “Contourlets provide a new system representation for image analysis [11], [19].”
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries (2006, background): “Also, with the growing realization that regular separable 1-D wavelets are inappropriate for handling images, several new tailored multiscale and directional redundant transforms were introduced, including the curvelet [11], [12], contourlet [13], [14], wedgelet [15], bandlet [16], [17], and the ste”
The redundant discrete wavelet transform and additive noise (2005, background): “That is, if Y = Fy and Y ′ = Y + X , where X is a noise signal, then ‖Fy′ − Y ′‖(2) is minimized if we reconstruct y as y′ = F̃ ∗Y ′ = F̃ ∗Y + F̃ ∗X as specified in (14) [11].”
Directional multiresolution image representations (2002, methodology): “Therefore, in compression applications it is normally replaced by subband coding or wavelet transform 0This chapter includes research conducted jointly with Martin Vetterli [56, 57].”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, background): “How can we wisely choose A to perform well on the signals we have in mind? One line of work considered choosing preconstructed dictionaries, such as undecimated wavelets [149], steerable wavelets [145, 37, 136], contourlets [38, 39, 40, 70, 71], curvelets [146, 12], and others [22, 123].”
Multifocus image fusion using the nonsubsampled contourlet transform (2009, methodology): “In recent years, Do and Vetterli developed a true 2-D image representation method, namely, the contourlet transform (CT) [12], which is achieved by combining the LP [6,13] and the directional filter bank (DFB) [14].”
Learning Multiscale Sparse Representations for Image and Video Restoration (2008, background): “Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA…”
Graph Regularized Sparse Coding for Image Representation (2011, background): “Traditionally, the dictionary is chosen from standard bases (e.g., wavelet [23], curvelet [24], contourlets [25], and bandlets [2]), or even generated from random matrices [26], [27].”
Sparse Representation for Color Image Restoration (2008, background): “If we consider the case where is the set of natural images, dictionaries such as wavelets of various sorts [4], curvelets [5], [6], contourlets [7], [8], wedgelets [9], bandlets [10], [11], and steerable wavelets [12], [13], are all attempts to design dictionaries that fulﬁll the above model…”
A Multiscale Pyramid Transform for Graph Signals (2013, background): “In this case, Do and Vetterli [49], [50] show that Burt and Adelson’s single-level synthesis operator is not optimal in terms of the reconstruction error.”
The Nonsubsampled Contourlet Transform: Theory, Design, and Applications (2006, methodology): “The contourlet transform [14] is a multidirectional and multiscale transform that is constructed by combining the Laplacian pyramid [16], [17] with the directional filter bank (DFB) proposed in [18].”
Why Simple Shrinkage Is Still Relevant for Redundant Representations? (2006, methodology): “Smoothness penalty P r fx x xg = kL L Lx x xk 2 2 using the Laplacian operator , leading to the Wiener filter ^ x x x = (I I I + L L L T L L L) 01 y y y. Manuscript received January 24, 2005; revised December 25, 2005.”