Signal unmixing analysis decomposes data into basic patterns and is widely applied in chemical and biological research. Multivariate curve resolution (MCR), a branch of signal unmixing, separates mixed signals into components (base patterns) and their concentrations (intensity), playing a key role in understanding composition. Classical MCR is typically framed as matrix factorization (MF) and requires a user-specified number of components, usually unknown in real data. Once data or component number increases, the scalability of these MCR approaches face significant challenges. This study reformulates MCR as a data generative process (gMCR), and introduces an Energy-Based solver, EB-gMCR, that automatically discovers the smallest component set and their concentrations for reconstructing the mixed signals faithfully. On synthetic benchmarks with up to 256 components, EB-gMCR attains high reconstruction fidelity and recovers the component count within 5% at 20dB noise and near-exact at 30dB. On two public spectral datasets, it identifies the correct component count and improves component separation over MF-based MCR approaches (NMF variants, ICA, MCR-ALS). EB-gMCR is a general solver for fixed-pattern signal unmixing (components remain invariant across mixtures). Domain priors (non-negativity, nonlinear mixing) enter as plug-in modules, enabling adaptation to new instruments or domains without altering the core selection learning step. The source code is available at https://github.com/b05611038/ebgmcr_solver.

翻译：信号解混分析将数据分解为基本模式，广泛应用于化学与生物学研究。多元曲线分辨（MCR）作为信号解混的一个分支，将混合信号分离为组分（基础模式）及其浓度（强度），在理解组成成分中起关键作用。经典MCR通常被构建为矩阵分解（MF）问题，需要用户指定组分数量，而实际数据中该数量通常是未知的。一旦数据或组分数量增加，这些MCR方法的可扩展性面临显著挑战。本研究将MCR重新构建为数据生成过程（gMCR），并引入一种基于能量的求解器——EB-gMCR，该求解器能自动发现最小的组分集合及其浓度，以高保真度重建混合信号。在包含多达256个组分的合成基准测试中，EB-gMCR实现了高重建保真度，在20dB噪声下恢复的组分数量误差在5%以内，在30dB噪声下接近精确。在两个公开光谱数据集上，该方法识别出正确的组分数量，并在组分分离性能上优于基于MF的MCR方法（NMF变体、ICA、MCR-ALS）。EB-gMCR是一种适用于固定模式信号解混（组分在不同混合物中保持不变）的通用求解器。领域先验（非负性、非线性混合）可作为插件模块集成，使其能够适应新仪器或领域，而无需改变核心选择学习步骤。源代码可在 https://github.com/b05611038/ebgmcr_solver 获取。