Background suppression for anomaly detection

1. A method for anomaly detection, comprising:

structuring a multi-channel spatial-temporal sequence as a four-dimensional array;

decomposing the four-dimensional array to form a low-rank component representing a background signal and a residual component representing anomalies for each time point of the multi-channel spatial-temporal sequence;

determining a sequence of anomaly maps by stacking the residual components at all time points together; and

identifying anomalies based on the sequence of anomaly maps.

2. The method as recited in claim 1 , wherein identifying the anomalies based on the sequence of anomaly maps further comprises:

identifying the anomalies in a hyperspectral imaging sequence.

3. The method as recited in claim 1 , further comprising:

implementing flattening to account for dependencies between different spatial locations and different channels.

4. The method as recited in claim 1 , wherein decomposing the four-dimensional array further comprises:

decomposing an input signal array X into two components: a low-rank component L and a residual component R,

wherein X=L+R, and

wherein L represents a projection of an original signal onto a background subspace, and R represents a background-suppressed signal of an anomaly target.

5. The method as recited in claim 1 , wherein decomposing the four-dimensional array further comprises:

assigning positive integer values that represent an estimated degree of variation of the background signal for each dimension.

6. The method as recited in claim 1 , wherein decomposing the four-dimensional array further comprises:

determining a set of basis that characterizes a variation of an input signal in each dimension; and

condensing an original signal into a coefficient representation with respect to the set of basis.

7. The method as recited in claim 6 , further comprising:

reconstructing an array including the input signal from a projection of an original signal onto a background subspace, wherein the reconstructed array is limited to information on the set of basis.

8. The method as recited in claim 1 , wherein structuring the multi-channel spatial-temporal sequence further comprises:

structuring a hyperspectral imaging sequence with two-dimensional spatial scenes.

9. The method as recited in claim 8 , wherein structuring the multi-channel spatial-temporal sequence further comprises:

implementing monitoring in agriculture and environment based on detecting at least one of nutrition, water deficiency of crops, and gas pipeline leakage.

10. The method as recited in claim 1 , further comprising:

determining at least one of daily or seasonal temperature variations and an inter-dependency between spatial locations and spectral bands.

11. The method as recited in claim 1 , wherein the four-dimensional array includes dimensions of distance, angle, frequency channel and time.

12. A computer system for anomaly detection, comprising:

a processor device operatively coupled to a memory device, the processor device being configured to:

structure a multi-channel spatial-temporal sequence as a four-dimensional array;

decompose the four-dimensional array to form a low-rank component representing a background signal and a residual component representing anomalies for each time point of the multi-channel spatial-temporal sequence;

determine a sequence of anomaly maps by stacking the residual components at all time points together; and

identify anomalies based on the sequence of anomaly maps.

13. The system as recited in claim 12 , wherein, when identifying the anomalies based on the sequence of anomaly maps, the processor device is further configured to:

identify the anomalies in a hyperspectral imaging sequence.

14. The system as recited in claim 12 , wherein the processor device is further configured to:

implement flattening to account for dependencies between different spatial locations and different channels.

15. The system as recited in claim 12 , wherein, when decomposing the four-dimensional array, the processor device is further configured to:

decompose an input signal array X into two components: a low-rank component L and a residual component R,

wherein X=L+R, and

wherein L represents a projection of an original signal onto a background subspace, and R represents a background-suppressed signal of an anomaly target.

16. The system as recited in claim 12 , wherein, when decomposing the four-dimensional array, the processor device is further configured to:

assign positive integer values that represent an estimated degree of variation of the background signal for each dimension.

17. The system as recited in claim 12 , wherein, when decomposing the four-dimensional array, the processor device is further configured to:

determine a set of basis that characterizes a variation of an input signal in each dimension; and

condense an original signal into a coefficient representation with respect to the set of basis.

18. The system as recited in claim 17 , wherein the processor device is further configured to:

reconstruct an array including the input signal from a projection of an original signal onto a background subspace, wherein the reconstructed array is limited to information on the set of basis.

19. The system as recited in claim 11 , wherein, when applying the NMT model to quantify strength of invariant relationship, the processor device is further configured to:

determining at least one of daily or seasonal temperature variations and an inter-dependency between spatial locations and spectral bands.