Randomized SVD Methods in Hyperspectral Imaging

Zhang, Jiani; Erway, Jennifer B.; Hu, Xuemei; Zhang, Qiang; Plemmons, Robert J.

doi:10.1155/2012/409357

Cited by 21 publications

(8 citation statements)

References 25 publications

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“…In case of the passive HS sensor, lighting conditions, altitude, azimuth of the sun and cloud shadows significantly reduce the time window for HS data collection [47]. The conditions of HS aerial data collection that determine data quality significantly limit the time window when it can be effectively collected [48].…”

Section: Airborne Laser Scanning Vs Hyperspectral Imagesmentioning

confidence: 99%

Multiple Flights or Single Flight Instrument Fusion of Hyperspectral and ALS Data? A Comparison of their Performance for Vegetation Mapping

Sławik

Niedzielko

Kania³

et al. 2019

Remote Sensing

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Fusion of remote sensing data often improves vegetation mapping, compared to using data from only a single source. The effectiveness of this fusion is subject to many factors, including the type of data, collection method, and purpose of the analysis. In this study, we compare the usefulness of hyperspectral (HS) and Airborne Laser System (ALS) data fusion acquired in separate flights, Multiple Flights Data Fusion (MFDF), and during a single flight through Instrument Fusion (IF) for the classification of non-forest vegetation. An area of 6.75 km2 was selected, where hyperspectral and ALS data was collected during two flights in 2015 and one flight in 2017. This data was used to classify three non-forest Natura 2000 habitats i.e., Xeric sand calcareous grasslands (code 6120), alluvial meadows of river valleys of the Cnidion dubii (code 6440), species-rich Nardus grasslands (code 6230) using a Random Forest classifier. Our findings show that it is not possible to determine which sensor, HS, or ALS used independently leads to a higher classification accuracy for investigated Natura 2000 habitats. Concurrently, increased stability and consistency of classification results was confirmed, regardless of the type of fusion used; IF, MFDF and varied information relevance of single sensor data. The research shows that the manner of data collection, using MFDF or IF, does not determine the level of relevance of ALS or HS data. The analysis of fusion effectiveness, gauged as the accuracy of the classification result and time consumed for data collection, has shown a superiority of IF over MFDF. IF delivered classification results that are more accurate compared to MFDF. IF is always cheaper than MFDF and the difference in effectiveness of both methods becomes more pronounced when the area of aerial data collection becomes larger.

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Section: Airborne Laser Scanning Vs Hyperspectral Imagesmentioning

confidence: 99%

Multiple Flights or Single Flight Instrument Fusion of Hyperspectral and ALS Data? A Comparison of their Performance for Vegetation Mapping

Sławik

Niedzielko

Kania³

et al. 2019

Remote Sensing

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“…To increase the accuracy of MRF, one will need an even finer dictionary with more elements and it will become increasingly more expensive to compute the SVD of such a dictionary. Methods such as the randomized SVD [29], [30] can be considered as a less expensive alternative to computing the SVD of a large matrix and have been shown to provide accurate decompositions for large matrices [31], [32]. However, it is worth emphasizing that this calculation only needs to be performed once for each imaging sequence, and thus computational speed is not as important in this step as in the pattern matching steps.…”

Section: Discussionmentioning

confidence: 99%

SVD Compression for Magnetic Resonance Fingerprinting in the Time Domain

McGivney

Pierre

et al. 2014

IEEE Trans. Med. Imaging

248

354

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Magnetic resonance fingerprinting is a technique for acquiring and processing MR data that simultaneously provides quantitative maps of different tissue parameters through a pattern recognition algorithm. A predefined dictionary models the possible signal evolutions simulated using the Bloch equations with different combinations of various MR parameters and pattern recognition is completed by computing the inner product between the observed signal and each of the predicted signals within the dictionary. Though this matching algorithm has been shown to accurately predict the MR parameters of interest, one desires a more efficient method to obtain the quantitative images. We propose to compress the dictionary using the singular value decomposition (SVD), which will provide a low-rank approximation. By compressing the size of the dictionary in the time domain, we are able to speed up the pattern recognition algorithm, by a factor of between 3.4-4.8, without sacrificing the high signal-to-noise ratio of the original scheme presented previously.

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“…The total cost of this algorithm to obtain rank k SVD including the operation count to obtain Q is O(mnlog(k) + k 2 (m + n)). Randomized SVD have also been studied and used in many applications [41,50,86,107,116,160,164]. Some other randomized algorithms for low rank approximation of a matrix have been proposed in [2] (sparsification), [16,152].…”

Section: (Iii) Randomized Svdmentioning

confidence: 99%

“…Randomized SVD have also been studied and used in many applications [41,50,86,107,116,160,164]. Some other randomized algorithms for low rank approximation of a matrix have been proposed in [2] (sparsification), [16,152].…”

Section: (Iii) Randomized Svdmentioning

confidence: 99%

Literature survey on low rank approximation of matrices

Кумар

Schneider

2016

Linear and Multilinear Algebra

115

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Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic algorithms for low rank approximation. But these techniques are very expensive (O(n 3 ) operations are required for n × n matrices). There are several randomized algorithms available in the literature which are not so expensive as the classical techniques (but the complexity is not linear in n). So, it is very expensive to construct the low rank approximation of a matrix if the dimension of the matrix is very large. There are alternative techniques like Cross/Skeleton approximation which gives the low-rank approximation with linear complexity in n. In this article we review low rank approximation techniques briefly and give extensive references of many techniques.

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Randomized SVD Methods in Hyperspectral Imaging

Cited by 21 publications

References 25 publications

Multiple Flights or Single Flight Instrument Fusion of Hyperspectral and ALS Data? A Comparison of their Performance for Vegetation Mapping

Multiple Flights or Single Flight Instrument Fusion of Hyperspectral and ALS Data? A Comparison of their Performance for Vegetation Mapping

SVD Compression for Magnetic Resonance Fingerprinting in the Time Domain

Literature survey on low rank approximation of matrices

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