Utilizing three‐dimensional wavelet transforms for accelerated evaluation of hyperspectral image cubes

Abstract

Hyperspectral imaging sensors are continuously enhanced by increasing spatial and spectral resolution. However, the 'curse of dimensionality' comes into effect, as the amount of acquired data increases in third order (two spatial, one spectral dimension). On top of that, the computational expense of many chemometric data evaluation techniques such as principal component analysis (PCA) rises also in third order with the data amount. Thus the need for computer memory is increased in third and the demand for computational power up to ninth order. One immediate consequence of massively increased computation times is a decreased time resolution of hyperspectral imagers, which is especially detrimental in online applications. Archiving humongous amounts of data becomes another burden. Thus it is anticipated that increased computation resources alone will not be able to facilitate fast online evaluation of hyperspectral data cubes or even to handle the acquired data. In this study, 3D wavelet transforms are used for compression of hyperspectral data cubes prior to chemometric data evaluation and/or data storage. Five different wavelet types of the Daubechies family are compared with respect to their ability to preserve relevant information in compressed data cubes. Because only relevant information has to be considered, shorter computation time and less storage space are required. By means of experimental hyperspectral data cubes it is demonstrated that additional computation expense for the 3D wavelet transform is largely overcompensated by reduced calculations necessitated by smaller data cubes. In the presented examples, computation time for a PCA could be decreased by one order of magnitude; storage space could be reduced to < 1% of the original size. It was found that the wavelet type has a major influence on the acceleration factors.

Imaging mass spectrometry data reduction: Automated feature identification and extraction

“…Note: This degree of reduction is probably an underestimate, reflecting the very low mass resolution of the original dataset, just 6490 samples spanning the m/z range 2800 -25,000. Three-dimensional wavelet based data reduction exceeding 100ϫ has been reported for hyperspectral imaging from focal plane array detectors [23]. When using wavelet-based data reduction techniques, any subsequent analysis is performed on the wavelet coefficients and not the measured masses.…”

Trilinear analysis of images obtained with a hyperspectral imaging confocal microscope

“…S/N increase should approach the square root of the compression factor for spatially uniform neighborhoods. Pixel binning also compares favorably with alternative spatial compression methods such as wavelet compression [25,28]. For instance, since variances add, simple pixel binning preserves the fundamental noise structure of the original data and uncorrelated noise remains uncorrelated.…”

Accelerating kernel principal component analysis (KPCA) by utilizing two‐dimensional wavelet compression: applications to spectroscopic imaging

“…In order to ensure a meaningful wavelet compression in the X-dimension [22][23][24][25], the same wavelet coefficients in the X-direction have to be removed from all rows of K. If this is not ensured, the subsequent WTs in the Y-dimension would incorporate wavelet coefficients belonging to different positions of the X-dimension WTs. This would cause the final result to be meaningless.…”

“…New approaches are required that enable diagonalization of such large matrices on personal computers within reasonable time. Already available wavelet-based compression methods [22][23][24][25] cannot be used since they load the full dataset and compress it while holding the entire dataset in memory. Here, this must be avoided at all times simply because of datasets sizes.…”

“…In order to handle large amounts of data in a timely fashion, multi-dimensional wavelet transformations (WTs) [13][14][15][16][17][18][19][20][21] have been employed as an effective method of data compression prior to chemometric computations [22][23][24][25] (and references therein). These techniques facilitate reductions in memory requirements and computation times.…”