Kronecker Compressive Sensing

By Marco F. Duarte, Richard Baraniuk. IEEE Transactions on Image Processing, 2012

537 citations recorded by the source corpus.

Compressive sensing (CS) is an emerging approach for the acquisition of signals having a sparse or compressible representation in some basis. While the CS literature has mostly focused on problems involving 1-D signals and 2-D images, many important applications involve multidimensional signals; the construction of sparsifying bases and measurement systems for such signals is complicated by their higher dimensionality. In this paper, we propose the use of Kronecker product matrices in CS for two purposes. First, such matrices can act as sparsifying bases that jointly model the structure present in all of the signal dimensions. Second, such matrices can represent the measurement protocols used in distributed settings. Our formulation enables the derivation of analytical bounds for the sparse approximation of multidimensional signals and CS recovery performance, as well as a means of evaluating novel distributed measurement schemes.

Subfields: Biomedical Engineering, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/9068b6930c7b26906c2636c390988ba733a481a9

How researchers see this paper

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

In Biomedical Engineering

1. Marco F. Duarte
2. Yonina C. Eldar
3. Lawrence Carin
4. David J. Brady
5. Andrzej S. Cichocki
6. Guoxu Zhou
7. Anh Huy Phan
8. Moshe Mishali

In Computational Mechanics

1. Marco F. Duarte
2. Yonina C. Eldar
3. Lawrence Carin
4. David J. Brady
5. Anh Huy Phan
6. David S. Kittle
7. Qibin Zhao
8. Andrzej S. Cichocki

In Electrical and Electronic Engineering

1. Marco F. Duarte
2. Yonina C. Eldar
3. Qibin Zhao
4. Lawrence Carin
5. Andrzej S. Cichocki
6. Gonzalo R. Arce
7. David J. Brady
8. Lieven De Lathauwer

Citations in the corpus

• Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, methodology): “In many applications, the dictionary and the sensing matrix admit a Kronecker structure (Kronecker-CS model), as illustrated in Figure 7 (top) [84].”
• Compressive Coded Aperture Spectral Imaging: An Introduction (2014, methodology): “IEEE SIGNAL PROCESSING MAGAZINE [108] JANUARY 2014 Kronecker basis 1 2 7 W W W = is often used, where 1 W is the two-dimensional-wavelet Symmlet-8 basis and 2 W is the cosine basis [17].”
• Structured Compressed Sensing: From Theory to Applications (2011, methodology): “Lemma 4 [96], [97]: Let , be bases for for .”