Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize

Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two nonnegative matrices. This property makes NMF well suited for unmixing grain-size distribution data, which are inherently nonnegative and have row sums equal to one. Previous studies have shown that AnalySize, an NMF-based method, performs well on poorly mixed grain-size distribution data but struggles when the data is highly mixed, where no observed samples are close to the true end members. To overcome this limitation, we introduce a maximum-distance NMF that encourages the estimated end members to be as distinct as possible and develop a hierarchical alternating least squares algorithm for optimization. The proposed formulation can be regarded as a generalization of AnalySize, where AnalySize minimizes the distance among end members while the proposed method maximizes it. Experimental results demonstrate that the method effectively decomposes highly mixed grain-size distribution data.

Beyond Unfolding: 60x Faster One-Stage Unmixing for Closely-Spaced Infrared Small Targets

Due to the optical diffraction limit and long imaging distances, Closely-Spaced Infrared Small Targets (CSIST) typically exhibit energy overlap, manifesting as indistinguishable blobs in infrared images. This ambiguity invalidates the one-to-one mapping assumption of traditional detection, thereby necessitating a paradigm shift towards CSIST Unmixing, which decomposes these blobs into discrete sub-targets. However, the dominant paradigm deep unfolding networks are shackled by the high latency and structural inflexibility intrinsic to their repetitively iterative architecture. To this end, we propose the Fast One-stage CSIST Unmixing Scheme (FOCUS), a one-stage lightweight paradigm which demonstrates that deep unfolding is not necessary. Motivated by the key observation that image super-resolution (SR) and CSIST Unmixing share an isomorphic degradation model, our insight is that it is possible to achieve a paradigm shift from image SR to CSIST Unmixing via completely transforming the label space, loss functions, and evaluation criteria. Specifically, to avoid entangling geometric recovery with artifact suppression, FOCUS adopts a single pass mapping with an internal coarse-to-fine flow that progressively refines target localization from coarse spatial distributions to finer sub-pixel precision. While sparsity regularization suppresses background clutter, it also attenuates target intensities. To compensate for this attenuation of valid signals, flux conservation is introduced as a competing constraint that restores signal energy back to target centers. To the best of our knowledge, this work is the first attempt to address this task via a lightweight one-stage framework without the DUN paradigm. Experiments demonstrate that our method matches or surpasses the state-of-the-art unfolding approaches in both localization and unmixing accuracy, while boosting the inference speed by 60x.