Alternating least squares within the multivariate curve resolution frameworkhas seen a lot of practical applications and shows their distinction with theirrelatively simple and flexible implementation. However, the limitations of leastsquares should be carefully considered when deviating from the standardassumed data structure. Within this work, we highlight the effects of noise inthe presence of minor components, and we propose a novel weighting schemewithin the weighted multivariate curve-resolution-alternating least squaresframework to resolve it. Two simulated and one Raman imaging case areinvestigated by comparing the novel methodology against standard multivari-ate curve resolution-alternating least squares and essential spectral pixel selec-tion. A trade-off is observed between current methods, whereas the novelweighting scheme demonstrates a balance where the benefits of the previoustwo methods are retained.