75 research outputs found
A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
Partially Coherent Ptychography by Gradient Decomposition of the Probe
Coherent ptychographic imaging experiments often discard over 99.9 % of the
flux from a light source to define the coherence of an illumination. Even when
coherent flux is sufficient, the stability required during an exposure is
another important limiting factor. Partial coherence analysis can considerably
reduce these limitations. A partially coherent illumination can often be
written as the superposition of a single coherent illumination convolved with a
separable translational kernel. In this paper we propose the Gradient
Decomposition of the Probe (GDP), a model that exploits translational kernel
separability, coupling the variances of the kernel with the transverse
coherence. We describe an efficient first-order splitting algorithm GDP-ADMM to
solve the proposed nonlinear optimization problem. Numerical experiments
demonstrate the effectiveness of the proposed method with Gaussian and binary
kernel functions in fly-scan measurements. Remarkably, GDP-ADMM produces
satisfactory results even when the ratio between kernel width and beam size is
more than one, or when the distance between successive acquisitions is twice as
large as the beam width.Comment: 11 pages, 9 figure
Non-convex approaches for low-rank tensor completion under tubal sampling
Tensor completion is an important problem in modern data analysis. In this
work, we investigate a specific sampling strategy, referred to as tubal
sampling. We propose two novel non-convex tensor completion frameworks that are
easy to implement, named tensor - (TL12) and tensor completion via
CUR (TCCUR). We test the efficiency of both methods on synthetic data and a
color image inpainting problem. Empirical results reveal a trade-off between
the accuracy and time efficiency of these two methods in a low sampling ratio.
Each of them outperforms some classical completion methods in at least one
aspect
Minimizing Quotient Regularization Model
Quotient regularization models (QRMs) are a class of powerful regularization
techniques that have gained considerable attention in recent years, due to
their ability to handle complex and highly nonlinear data sets. However, the
nonconvex nature of QRM poses a significant challenge in finding its optimal
solution. We are interested in scenarios where both the numerator and the
denominator of QRM are absolutely one-homogeneous functions, which is widely
applicable in the fields of signal processing and image processing. In this
paper, we utilize a gradient flow to minimize such QRM in combination with a
quadratic data fidelity term. Our scheme involves solving a convex problem
iteratively.The convergence analysis is conducted on a modified scheme in a
continuous formulation, showing the convergence to a stationary point.
Numerical experiments demonstrate the effectiveness of the proposed algorithm
in terms of accuracy, outperforming the state-of-the-art QRM solvers.Comment: 20 page
Improvements on Uncertainty Quantification for Node Classification via Distance-Based Regularization
Deep neural networks have achieved significant success in the last decades,
but they are not well-calibrated and often produce unreliable predictions. A
large number of literature relies on uncertainty quantification to evaluate the
reliability of a learning model, which is particularly important for
applications of out-of-distribution (OOD) detection and misclassification
detection. We are interested in uncertainty quantification for interdependent
node-level classification. We start our analysis based on graph posterior
networks (GPNs) that optimize the uncertainty cross-entropy (UCE)-based loss
function. We describe the theoretical limitations of the widely-used UCE loss.
To alleviate the identified drawbacks, we propose a distance-based
regularization that encourages clustered OOD nodes to remain clustered in the
latent space. We conduct extensive comparison experiments on eight standard
datasets and demonstrate that the proposed regularization outperforms the
state-of-the-art in both OOD detection and misclassification detection.Comment: Neurips 202
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