Search

Optical imaging of calcium signals in the brain has enabled researchers to observe the activity of hundreds-to-thousands of individual neurons simultaneously. Current methods predominantly use morphological information, typically focusing on expected shapes of cell bodies, to better identify neurons in the field-of-view. The explicit shape constraints limit the applicability of automated cell identification to other important imaging scales with more complex morphologies, e.g., dendritic or widefield imaging. Specifically, fluorescing components may be broken up, incompletely found, or merged in ways that do not accurately describe the underlying neural activity. Here we present Graph Filtered Temporal Dictionary (GraFT), a new approach that frames the problem of isolating independent fluorescing components as a dictionary learning problem. Specifically, we focus on the time-traces—the main quantity used in scientific discovery—and learn a time trace dictionary with the spatial maps acting as the presence coefficients encoding which pixels the time-traces are active in. Furthermore, we present a novel graph filtering model which redefines connectivity between pixels in terms of their shared temporal activity, rather than spatial proximity. This model greatly eases the ability of our method to handle data with complex non-local spatial structure. We demonstrate important properties of our method, such as robustness to morphology, simultaneously detecting different neuronal types, and implicitly inferring number of neurons, on both synthetic data and real data examples. Specifically, we demonstrate applications of our method to calcium imaging both at the dendritic, somatic, and widefield scales.

Despite the importance of sparsity signal models and the increasing prevalence of high-dimensional streaming data, there are relatively few algorithms for dynamic filtering of time-varying sparse signals. Of the existing algorithms, fewer still provide strong performance guarantees. This paper examines two algorithms for dynamic filtering of sparse signals that are based on efficient $\ell _1$ optimization methods. We first present an analysis for one simple algorithm (BPDN-DF) that works well when the system dynamics are known exactly. We then introduce a novel second algorithm (RWL1-DF) that is more computationally complex than BPDN-DF but performs better in practice, especially in the case where the system dynamics model is inaccurate. Robustness to model inaccuracy is achieved by using a hierarchical probabilistic data model and propagating higher-order statistics from the previous estimate (akin to Kalman filtering) in the sparse inference process. We demonstrate the properties of these algorithms on both simulated data as well as natural video sequences. Taken together, the algorithms presented in this paper represent the first strong performance analysis of dynamic filtering algorithms for time-varying sparse signals as well as state-of-the-art performance in this emerging application.

Tracking algorithms such as the Kalman filter aim to improve inference performance by leveraging the temporal dynamics in streaming observations. However, the tracking regularizers are often based on the $\ell_p$-norm which cannot account for important geometrical relationships between neighboring signal elements. We propose a practical approach to using the earth mover's distance (EMD) via the earth mover's distance dynamic filtering (EMD-DF) algorithm for causally tracking time-varying sparse signals when there is a natural geometry to the coefficient space that should be respected (e.g., meaningful ordering). Specifically, this paper presents a new Beckmann formulation that dramatically reduces computational complexity, as well as an evaluation of the performance and complexity of the proposed approach in imaging and frequency tracking applications with real and simulated neurophysiology data., Comment: 5 pages, 3 figures

Sparsity-based models have enabled significant advances in many image processing tasks. Hyperspectral imagery (HSI) in particular has benefited from these approaches due to the significant low-dimensional structure in both spatial and spectral dimensions. Specifically, previous work has shown that sparsity models can be used for spectral superresolution, where spectral signatures with HSI-level resolution are recovered from measurements with multispectral-level resolution (i.e., an order of magnitude fewer spectral bands). In this letter, we expand on those results by introducing a new inference approach known as reweighted l1 spatial filtering (RWL1-SF). RWL1-SF incorporates a more sophisticated signal model that allows for variations in the SNR at each pixel as well as spatial dependences between neighboring pixels. The results demonstrate that the proposed approach leverages signal structure beyond simple sparsity to achieve significant improvements in spectral superresolution.

Compressed sensing is an important application in signal and image processing which requires solving nonlinear optimization problems. A Hopfield-Network-like analog system is proposed as a solution, using the locally competitive algorithm (LCA) to solve an overcomplete l1 sparse approximation problem. A scalable system architecture using sub-threshold currents is described, including vector matrix multipliers (VMMs) and a nonlinear thresholder. A 4 × 6 nonlinear system is implemented on the RASP 2.9v chip, a field programmable analog array with directly programmable floating gate elements, allowing highly accurate VMMs. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% rms, and an objective value only 1.3% higher on average. The active circuit consumed 29 μA of current at 2.4 V, and converges on solutions in 240 μs. A smaller 2 × 3 system is also implemented. Extrapolating the scaling trends to a N=1000 node system, the analog LCA compares favorably with state-of-the-art digital solutions, using a small fraction of the power to arrive at solutions ten times faster. Finally, we provide simulations of large scale systems to show the behavior of the system scaled to nontrivial problem sizes.

The spectral features in hyperspectral imagery (HSI) contain significant structure that, if properly characterized, could enable more efficient data acquisition and improved data analysis. Because most pixels contain reflectances of just a few materials, we propose that a sparse coding model is well-matched to HSI data. Sparsity models consider each pixel as a combination of just a few elements from a larger dictionary, and this approach has proven effective in a wide range of applications. Furthermore, previous work has shown that optimal sparse coding dictionaries can be learned from a dataset with no other a priori information (in contrast to many HSI “endmember” discovery algorithms that assume the presence of pure spectra or side information). We modified an existing unsupervised learning approach and applied it to HSI data (with significant ground truth labeling) to learn an optimal sparse coding dictionary. Using this learned dictionary, we demonstrate three main findings: 1) the sparse coding model learns spectral signatures of materials in the scene and locally approximates nonlinear manifolds for individual materials; 2) this learned dictionary can be used to infer HSI-resolution data with very high accuracy from simulated imagery collected at multispectral-level resolution, and 3) this learned dictionary improves the performance of a supervised classification algorithm, both in terms of the classifier complexity and generalization from very small training sets.

Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neurons demonstrate over-dispersed spiking behaviour. Although the Negative Binomial Generalized Linear Model (NB-GLM) provides a powerful tool for modeling over-dispersed spike counts, the maximum likelihood-based standard NB-GLM leads to highly variable and inaccurate parameter estimates. Thus, we propose a hierarchical parametric empirical Bayes method to estimate the neural spike responses among neuronal population. Our method integrates both Generalized Linear Models (GLMs) and empirical Bayes theory, which aims to (1) improve the accuracy and reliability of parameter estimation, compared to the maximum likelihood-based method for NB-GLM and Poisson-GLM; (2) effectively capture the over-dispersion nature of spike counts from both simulated data and experimental data; and (3) provide insight into both neural interactions and spiking behaviours of the neuronal populations. We apply our approach to study both simulated data and experimental neural data. The estimation of simulation data indicates that the new framework can accurately predict mean spike counts simulated from different models and recover the connectivity weights among neural populations. The estimation based on retinal neurons demonstrate the proposed method outperforms both NB-GLM and Poisson-GLM in terms of the predictive log-likelihood of held-out data. Codes are available in https://doi.org/10.5281/zenodo.4704423, Comment: 16 pages, 20 figures, 3 tables