Code for the paper "Anomaly Detection in Images With Smooth Background via Smooth-Sparse Decomposition".

Here is the Link to the paper. This repository provides a MATLAB implementation of the paper.

• bsplineBasis.m: Function to generate bsplineBasis with k Bspline Basis and n grids with degree sd and boundary degree bd

  • By default bd=sd-1
  • Cubic B-spline, we set sd=3

• bsplineSmoothDecompauto: The major function:

  • Input variable
    • y : Signal/image to be decomposed
    • B : Basis for mean
    • Ba : Basis for anomalies
    • lambda : Smoothing Parameter, the algorithm will decide if empty
    • gamma : Sparsity Parameter, the algorithm will decide if empty
  • Output variable:
    • yhat : mean
    • a : Anomalies

• main.m: Test function, use the information in data.mat to generate a simulation. The result of estimated and true anomalies are quite similar.

Practical Advices:

• Choosing the knot of basis is very important especially on the two parameters skx and sky and these should really come from the domain knowledge.
• The current algorithm works better if you use smaller basis Bs to cover larger anomaly. Using too large of basis could lead to a bad estimation of the exact shape.
• Using small basis is typically not very robust to noise. If you have very noisy image, consider using larger basis (fewer knots B-spline basis. )

Reference: Yan, H., Paynabar, K., & Shi, J. (2017). Anomaly detection in images with smooth background via smooth-sparse decomposition. Technometrics, 59(1), 102-114.