@conference {65048, title = {Sparse LMS via online linearized Bregman iteration.}, booktitle = {ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year = {2014}, month = {2014 Jul 14}, publisher = {IEEE}, organization = {IEEE}, address = {Florence, Italy}, abstract = {

We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l\ 1\ -l\ 2\ norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and derive theoretical expressions for the steady state mean square deviations (MSD). We demonstrate numerically that OLBI improves the performance of LMS type algorithms for signals generated from sparse tap weights.

}, doi = {10.1109/ICASSP.2014.6855000}, url = {http://ieeexplore.ieee.org/document/6855000/http://xplorestaging.ieee.org/ielx7/6844297/6853544/06855000.pdf?arnumber=6855000}, author = {Hu, Tao and Chklovskii, Dmitri B.} } @article {6676, title = {Electron microscopy reconstruction of brain structure using sparse representations over learned dictionaries.}, journal = {IEEE Transactions on Medical Imaging}, volume = {32}, year = {2013}, month = {2013 Aug 2}, pages = {2179-88}, abstract = {

A central problem in neuroscience is reconstructing neuronal circuits on the synapse level. Due to a wide range of scales in brain architecture such reconstruction requires imaging that is both high-resolution and high-throughput. Existing electron microscopy (EM) techniques possess required resolution in the lateral plane and either high-throughput or high depth resolution but not both. Here, we exploit recent advances in unsupervised learning and signal processing to obtain high depth-resolution EM images computationally without sacrificing throughput. First, we show that the brain tissue can be represented as a sparse linear combination of localized basis functions that are learned using high-resolution datasets. We then develop compressive sensing-inspired techniques that can reconstruct the brain tissue from very few (typically 5) tomographic views of each section. This enables tracing of neuronal processes and, hence, high throughput reconstruction of neural circuits on the level of individual synapses.

}, issn = {1558-254X}, doi = {10.1109/TMI.2013.2276018}, author = {Hu, Tao and Nunez-Iglesias, Juan and Vitaladevuni, Shiv and Scheffer, Lou and Xu, Shan and Bolorizadeh, Mehdi and Hess, Harald and Fetter, Richard and Chklovskii, Dmitri} } @article {6220, title = {A network of spiking neurons for computing sparse representations in an energy-efficient way.}, journal = {Neural computation}, volume = {24}, year = {2012}, month = {2012 Nov}, pages = {2852-72}, abstract = {Computing sparse redundant representations is an important problem in both applied mathematics and neuroscience. In many applications, this problem must be solved in an energy-efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating by low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, the operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime, the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise; specifically, the representation error decays as 1/√t for gaussian white noise.}, keywords = {Action Potentials, Algorithms, Models, Neural Networks (Computer), Neurological, Neurons}, issn = {1530-888X}, doi = {10.1162/NECO_a_00353}, author = {Hu, Tao and Genkin, Alexander and Chklovskii, Dmitri B} } @article {4325, title = {High resolution segmentation of neuronal tissues from low depth-resolution EM imagery.}, journal = {8th International Conference of Energy Minimization Methods in Computer Vision and Pattern Recognition Energy Minimization Methods in Computer Vision and Pattern Recognition}, volume = {6819}, year = {2011}, month = {2011}, pages = {261-72}, abstract = {

The challenge of recovering the topology of massive neuronal circuits can potentially be met by high throughput Electron Microscopy (EM) imagery. Segmenting a 3-dimensional stack of EM images into the individual neurons is difficult, due to the low depth-resolution in existing high-throughput EM technology, such as serial section Transmission EM (ssTEM). In this paper we propose methods for detecting the high resolution locations of membranes from low depth-resolution images. We approach this problem using both a method that learns a discriminative, over-complete dictionary and a kernel SVM. We test this approach on tomographic sections produced in simulations from high resolution Focused Ion Beam (FIB) images and on low depth-resolution images acquired with ssTEM and evaluate our results by comparing it to manual labeling of this data.

}, issn = {978-3-642-23093-6}, author = {Glasner, Daniel and Hu, Tao and Nunez-Iglesias, Juan and Scheffer, Lou and Xu, CS and Hess, Harald and Fetter, Richard and Chklovskii, Dmitri and Basri, Ronen} } @article {1235, title = {Ultrastructural analysis of hippocampal neuropil from the connectomics perspective.}, journal = {Neuron}, volume = {67}, year = {2010}, month = {2010 Sep 23}, pages = {1009-20}, abstract = {

Complete reconstructions of vertebrate neuronal circuits on the synaptic level require new approaches. Here, serial section transmission electron microscopy was automated to densely reconstruct four volumes, totaling 670 μm(3), from the rat hippocampus as proving grounds to determine when axo-dendritic proximities predict synapses. First, in contrast with Peters{\textquoteright} rule, the density of axons within reach of dendritic spines did not predict synaptic density along dendrites because the fraction of axons making synapses was variable. Second, an axo-dendritic touch did not predict a synapse; nevertheless, the density of synapses along a hippocampal dendrite appeared to be a universal fraction, 0.2, of the density of touches. Finally, the largest touch between an axonal bouton and spine indicated the site of actual synapses with about 80\% precision but would miss about half of all synapses. Thus, it will be difficult to predict synaptic connectivity using data sets missing ultrastructural details that distinguish between axo-dendritic touches and bona fide synapses.

}, keywords = {Animals, Automatic Data Processing, Axons, Dendrites, Electron, Hippocampus, Long-Evans, Male, Microscopy, Neuropil, Newborn, Rats, Synapses, Transmission}, issn = {1097-4199}, doi = {10.1371/journal.pcbi.1001066}, author = {Mishchenko, Yuriy and Hu, Tao and Spacek, Josef and Mendenhall, John and Harris, Kristen M and Chklovskii, Dmitri B} } @article {1246, title = {Reconstruction of sparse circuits using multi-neuronal excitation (RESCUME).}, journal = {Neural Information Processing Systems}, volume = {22}, year = {2009}, month = {2009}, pages = {790-8}, abstract = {

One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. Reconstructing a large neural circuit using such a "brute force" approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron{\textquoteright}s voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. To reconstruct these synaptic connections from the recorded voltage we apply a decoding algorithm recently developed for compressive sensing. Compared to the brute force approach, our method promises significant time savings that grow with the size of the circuit. We use computer simulations to find optimal stimulation parameters and explore the feasibility of our reconstruction method under realistic experimental conditions including noise and non-linear synaptic integration. Multineuronal stimulation allows reconstructing synaptic connectivity just from the spiking activity of post-synaptic neurons, even when sub-threshold voltage is unavailable. By using calcium indicators, voltage-sensitive dyes, or multi-electrode arrays one could monitor activity of multiple postsynaptic neurons simultaneously, thus mapping their synaptic inputs in parallel, potentially reconstructing a complete neural circuit.

}, author = {Hu, Tao and Chklovskii, Dmitri B} }