Multiresolution Matrix Compression

The theory of matrix-valued multiresolution analysis frames

The Inversion of Poisson’s Integral in the Wavelet Domain

A wavelet transform algorithm combined with a conjugate gradient method is used for the inversion of Poisson’s integral (downward continuation), used in airborne gravimetry applications. The wavelet approximation is dependent on orthogonal wavelet base functions. The integrals are approximated in finite multiresolution analysis subspaces. Mallat’s algorithm is used in the multiresolution analys...

Learning-based multiresolution transforms with application to image compression

In Harten’s framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact and predicted values. In this paper we use tools of statistical learning in order to design a more accurate prediction operator ...

Multiresolution Matrix Factorization

Large matrices appearing in machine learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecomposition. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolu...

SVD-Wavelet Algorithm for image compression

We explore the use of the singular value decomposition (SVD) in image compression. We link the SVD and the multiresolution algorithms. In [22] it is derived a multiresolution representation of the SVD decomposition, and in [15] the SVD algorithm and Wavelets are linked, proposing a mixed algorithm which roughly consist on applying firstly a discrete Wavelet transform and secondly the SVD algori...