Comparing Different Unmixing Methods for weed detection and identification

Herbicides are extensively used for weed management worldwide. However, their use is a significant cause 
of environmental pollution and human health problems. Efficient Site-Specific weed management (SSWM) 
practice attempts to reduce herbicide use and its negative impacts by adjusting herbicide application based 
on weed composition and coverage. Such an application requires high-resolution data in spatial and spectral 
domains, which is not always available. Consequently, Mixed pixels are likely to exist, creating a challenge 
to generate accurate weed maps. In this regard, Spectral Mixture Analysis (SMA) can mitigate this challenge
by exploiting subpixel information. This study assesses the potential benefits of four SMA methods for 
estimating weed coverage of different botanical groups. We examined four methods- Constrained Least 
Squares Unmixing (FCLSU), Sparse Unmixing via variable Splitting and Augmented Lagrangian (SUnSAL), 
Sparse Unmixing via variable Splitting and Augmented Lagrangian and Total variation (SUnSAL-TV) and 
the Vectorized Code Projected Gradient Descent Unmixing (VPGDU). Each suggests a distinct advantage 
for spectral unmixing. We used controlled hyperspectral and multispectral field datasets to compare the four 
methods. The controlled data included weed species characterized by distinct botanical groups, while the 
field dataset included a corn field with weeds at varying densities. We assessed the performance of the 
different methods in estimating weed coverage and composition at various spatial resolutions. Our results
demonstrated the advantages of the total variation regularization of SUnSAL-TV and the superiority of the 
SAM-based method, VPGDU, over other approaches. VPGDU was the best-performing method, with MAE 
values consistently lower than 8.6% at all resolutions, underscoring the advantage of its objective function 
in unmixing weed botanical groups and the significant effect of illumination on the results. This result was 
also consistent in the field data as VPGDU yielded the lowest MAE of 11.95%,