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Marine oil spills have caused severe environmental pollution with long-term toxic effects on marine ecosystems and coastal habitants. Hyperspectral remote sensing is currently used in efforts to respond to oil spills. Spectral unmixing plays a key role in hyperspectral imaging because of its ability to extract accurate fractional abundances of constituent materials from spectrums collected by sensors. However, multiple oil-propagating processes provide different mixing states of oil and water, thereby involving complicated, nonlinear mixing effects between in-depth elements in water, especially those with a low concentration. Therefore, an accurate inversion of material abundance remains a challenging yet fundamental task. This study proposes an unmixing method with normalizers in a combined polynomial and sine model to resolve overfitting problems. An energy information-based wavelet package scheme effectively highlights the latent information of the concerned material. Experimental analyses of synthetic and real data indicate that the proposed method shows superior unmixing performance, especially in delivering more accurate abundance estimations of different background oil concentration levels as low as a fractional abundance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></semantics></math></inline-formula>, and can be used for long-term monitoring of oil propagation.