# total variation

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## total variation

[′tōd·əl ‚ver·ē′ā·shən]
(mathematics)
For a real function defined on an interval, the least upper bound of the function's variation relative to all possible partitions of the interval.
References in periodicals archive ?
High Value Revenues: 1,787.6 million euro (+6.2% total variation) thanks to its strengthening in all regions.
In PC 1 with eigenvalue of 0.653659 accounted for 10.607% of the total variability followed by PC 2 with eigenvalue 0.6069 accounted for 9.8483% of the total variation observed among the 64 walnut cultivars.
Total variation denoising techniques assume that images affected by noise have high total variation or the integral of its absolute gradient is high and therefore attempt to reduce the total variation.
This criterion establishes that a number of principal components should be retained, covering at least 70 to 90% of the total variation. After selecting the number of PCs, were obtained their respective eigenvalues, with their corresponding eigenvectors.
Thereby, Table 4 shows that the first axis of the PC correlated mainly with fruit diameter (0.369) and fruit length (0.366), with 52.08% of the total variation. The second axis of PC, with 21.36% of total variation, was strongly correlated in module with soluble solids (-0.471) and fruit mass (-0.454).
This value is a ratio of variation due to the measurement error (repeatability and reproducibility) to total variation of the system, including both part and measurement variation (FIGURE 1).
Morphological component analysis (MCA) theory is adopted for the image layer decomposition of IHI data, which is proposed in 2015 ; IMCA(Improved MCA) algorithm is proposed in , which is improved according to the IHI data's special characteristics; In , idea of MCA and Total Variation (TV) is combined and an IMT (Improved MCA-TV) algorithm is proposed for decomposition of the IHI data.
Among his topics are general Markov chains: ergodicity in total variation, weak ergodic states, and functional limit theorems.
In discriminant function analysis (DFA), the first two discriminant functions accounted for 72.00% of total variation, and discriminated fish samples into three major groups following to their collecting drainages.
One of the most popular regularizers is total variation (TV) of images (e.g., [21-23]), which helps to reduce ringing artifacts and noises in images while preserving the edges [21, 24].
As shown in Figure 3, we firstly implemented the image structure extraction method based on the image total variation to extract the structure of input images, which aims to smooth the image texture and reduce image noise.

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