I. INTRODUCTION  
II. COMPACT SOURCES IN MULTI-CHANNEL OBSERVATIONS  
A. Notation  
III. BASIC MULTI-CHANNEL DETECTION  
IV. MATRIX MULTI-FILTERS  
V. MATCHED MULTI-FILTER  
VI. BAYESIAN MULTICHANNEL DETECTION AND ESTIMATION  
A. Likelihood  
B. Priors  
C. Bayesian detection methods in the literature  
VII. POLARIZED SOURCES  
VIII. FINAL REMARKS