January 2023 addition:

For the majority of users working with time series of InSAR data, LiCSAlert is now recomended over calling ICASAR directly. LiCSAlert handles all aspects of calling ICASAR, and provides far more information to analyse a time series.

For users applying this algorithm to time series of data at pionts that can't be represented as images (e.g. recordings from 4 microphones in a room, results from seismometers etc.), ICASAR is still supported with examples included. This is similar to the method described in Turner et al. (2002) Stresses in the Lunar Interior: Insights From Slip Directions in the A01 Deep Moonquake Nest

ICASAR

An algorithm for robustly appling sICA to InSAR data in order to isolate deformation signals and atmospheric signals.

Gaddes et al., 2019 details its application to Sierra Negra (Galapagos Archipelago, Ecuador), where it was able to isolate the caldera floor uplift signal (source 1), and a topograhically correlated atmospheric phase screen (source 2):

The algorithm also provides tools to visualise the recovered sources in order for a user to determine how robust they are. Note that the sources capturing the caldera floor uplift (blue points), form an isolated and compact cluster:

Spring 2022 addition:

Previous version of ICASAR either performed sICA (i.e recovered spatially independent sources) for time series of interferograms, or preformed tICA (i.e. recovered temporally independent sources) for collections of 1D time series (e.g. five microphone recordings - see September 2020 addition). However, time series of interferograms can also be considered as a collection of 1D time series at each pixel, and therefore these can be treated as linear combinations of latent temporal signals (e.g. a pixel may experience both linear subsidence and seasonal uplift/subsidence, which could be decomposed into two latent sources). To address this, the spatial data example (i.e. a time series of interferograms) has now been updated to use ICASAR's new ability to perform tICA. In the ICASAR_settings dictionary, this is controlled with:

'sica_tica' : 'tica', # 'sica' for original sICA, 'tica' for tICA.

Note that in this case, the ifgs_format argument is redundant, as the cumulative displacement is always considered for a single pixel. When preforming sICA, ifgs_format can be varied to increase the variance of a deformation signal, as the signal is likely to be easier to see in the cumulative (long temporal baseline) interferograms, or by making all interferograms:

ifgs_format" : 'inc', # 'inc' for incremental (daisy chain) / 'cum' for cumulative (relative to first acquisition) / 'all' for between all acquisitions (only max_n_ifgs are made as this is a huge number of interferograms for long time series (N**2 - N for N acquisitions).

April 2021 addition:

To deal with small signals (i.e. ones that are not visible in a single 12 day Sentinel-1 interferogram), we can aid the isolation of these signals through computing all the possible interferograms between the acquisitions (i.e. to include many longer temporal baseline interferograms). This allows for the correlations between the strength with which an IC is used for a given interferograms, and its temporal baseline. ICs that contain deformation are likely to be used strongly in long temporal baseline interferograms. This figure also computes the correlations between ICS and the DEM, which is useful for determining if a signal captures a topographically correlated atmospheric phase screen.

August 2020 addition:

If both bootsrapped and non-bootstrapped runs are done in the same step, these can be displayed in the same plot. Note that the non-boostrapped runs generally create very small/tight clusters (as the sources recovered are generally very similar), and it can be difficult to achieve reasonable clutering results due to two scales of clusters present. In the example below, many sources recovered during bootstrapped runs ('o's) are marked as noise as they lie outside the compact clusters formed by the bootstrapped data ('x's):

June 2020 addition:

If longitude and latitude information for the interferograms is available, the independent components that are found can be geocoded and displayed in Google Earth:

September 2020 addition:

ICASAR now supports temporal data. Whilst this requires no changes to the heart of the algorithm, it required many changes to the plotting functionality, and the creation of a temporal example. The interactive plot (when hovering over a data point, more information is presented in an inset axes) is now a stand-alone function, for use with any data (link).

Presented with a set of mixtures created from an unknown number (but assumed to be less than the number of mixtures) of unknown sources:

The ICASAR algorithm returns an interactive figure which suggests that there are three latent sources (the compact and isolated clusters), and a noise term that is being interpreted as two clusters:

The three latent sources and two noise sources can be visualised. For further analysis, the noise terms can be discarded.

This contrasts with the results of FastICA, which doesn't provide any information as to which recovered sources capture the latent sources, and which capture the noise terms.