Name
Abstract | ||
|---|---|---|
This paper considers the spark of L × N submatrices of the N × N Discrete Fourier Transform (DFT) matrix. Here a matrix has spark m if every collection of its m - 1 columns are linearly independent. The motivation comes from such applications of compressed sensing as MRI and synthetic aperture radar, where device physics dictates the measurements to be Fourier samples of the signal. Consequently the observation matrix comprises certain rows of the DFT matrix. To recover an arbitrary k-sparse signal, the spark of the observation matrix must exceed 2k + 1. The technical question addressed in this paper is how to choose the rows of the DFT matrix so that its spark equals the maximum possible value L + 1. We expose certain coprimeness conditions that guarantee such a property. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/SAM.2014.6882460 | Sensor Array and Multichannel Signal Processing Workshop |
Keywords | Field | DocType |
discrete Fourier transforms,matrix algebra,signal sampling,sparse matrices,DFT matrix,Fourier sample measurements,Fourier sampling,L×N submatrices,MRI,N×N discrete Fourier transform,arbitrary k-sparse signal recovery,compressed sensing,coprime conditions,observation matrix,synthetic aperture radar,Coprime sensing,compressed sensing,full spark,vanishing sums | Mathematical optimization,Spark (mathematics),Matrix (mathematics),Computer science,Mathematical analysis,Computer network,Fourier transform,Discrete Fourier transform,Block matrix,Compressed sensing,Sparse matrix,DFT matrix | Conference |
ISSN | Citations | PageRank |
1551-2282 | 3 | 0.40 |
References | Authors | |
8 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Achanta, H.K. | 1 | 5 | 1.58 |
| Satyendra N. Biswas | 2 | 5 | 4.56 |
| Soura Dasgupta | 3 | 679 | 96.96 |
| Mathews Jacob | 4 | 790 | 59.62 |