@ARTICLE\{IMM2007-04695,
    author       = "A. A. Nielsen",
    title        = "The Regularized Iteratively Reweighted {MAD} Method for Change Detection in Multi- and Hyperspectral Data",
    year         = "2007",
    month        = "feb",
    keywords     = "remote sensing; canonical correlation analysis; {MAD} transformation; {IR-MAD}; regularization or penalization",
    pages        = "463-478",
    journal      = "{IEEE} Transactions on Image Processing",
    volume       = "16",
    editor       = "",
    number       = "2",
    publisher    = "",
    note         = "Matlab code in zip file here, {ENVI}/{IDL} and Python code including code for interaction with the Google Earth Engine on Dr. Morton J. Canty's home page. - Typo: in page 472, column {2,} second paragraph just below Fig. 17 should start wih: {''}Figure 21(a) shows the regularized {IR-MAD} variates 43, 42, and 41 as {RGB}.''",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4695-full.html",
    abstract     = "This paper describes new extensions to the previously published multivariate alteration detection (MAD) method for change detection in bi-temporal, multi- and hypervariate data such as remote sensing imagery. Much like boosting methods often applied in data mining work, the iteratively reweighted (IR) {MAD} method in a series of iterations places increasing focus on “difficult” observations, here observations whose change status over time is uncertain. The {MAD} method is based on the established technique of canonical correlation analysis: for the multivariate data acquired at two points in time and covering the same geographical region, we calculate the canonical variates and subtract them from each other. These orthogonal differences contain maximum information on joint change in all variables (spectral bands). The change detected in this fashion is invariant to separate linear (affine) transformations in the originally measured variables at the two points in time such as 1) changes in gain and offset in the measuring device used to acquire the data; 2) data normalization or calibration schemes that are linear (affine) in the gray values of the original variables; or 3) orthogonal or other affine transformations such as principal component (PC) or maximum autocorrelation factor (MAF) transformations. The {IR-MAD} method first calculates ordinary canonical and original {MAD} variates. In the following iterations we apply different weights to the observations, large weights are assigned to observations that show little change, i.e., for which the sum of squared, standardized {MAD} variates is small, and small weights are assigned to observations for which the sum is large. Like the original {MAD} method, the iterative extension is invariant to linear (affine) transformations of the original variables. To stabilize solutions to the (IR-){MAD} problem some form of regularization may be needed. This is especially useful for work on hyperspectral data. The paper describes ordinary two-set canonical correlation analysis, the {MAD} transformation, the iterative extension and three regularization schemes. A simple case with real Landsat Thematic Mapper (TM) data at one point in time and (partly) constructed data at the other point in time that demonstrates the superiority of the iterative scheme over the original {MAD} method is shown. Also, examples with {SPOT} High Resolution Visible (HRV) data from an agricultural region in Kenya, and hyperspectral airborne HyMap data from a small rural area in southeastern Germany are given. The latter case demonstrates the need for regularization.",
    isbn_issn    = "DOI:10.1109/TIP.2006.888195"
}