It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained l1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms l1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted l1-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations—not by reweighting the l1 norm of the coefficient sequence as is common, but by reweighting the l1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as Compressive Sensing.

/pdf/enhancing-sparsity-by-reweighted-l-1-minimization-znwoz4koxr.pdf

Enhancing Sparsity by Reweighted ℓ 1 Minimization

http://reuter.mit.edu/papers/reuter-robreg10.pdf

Highly accurate inverse consistent registration: a robust approach.

Continuous change detection and classification of land cover using all available Landsat data

During the course of a lifetime, somatic cells acquire mutations. Different mutational processes may contribute to the mutations accumulated in a cell, with each imprinting a mutational signature on the cell's genome. Some processes generate mutations throughout life at a constant rate in all individuals, and the number of mutations in a cell attributable to these processes will be proportional to the chronological age of the person. Using mutations from 10,250 cancer genomes across 36 cancer types, we investigated clock-like mutational processes that have been operating in normal human cells. Two mutational signatures show clock-like properties. Both exhibit different mutation rates in different tissues. However, their mutation rates are not correlated, indicating that the underlying processes are subject to different biological influences. For one signature, the rate of cell division may influence its mutation rate. This study provides the first survey of clock-like mutational processes operating in human somatic cells.

/pdf/clock-like-mutational-processes-in-human-somatic-cells-1qartswuza.pdf

Clock-like mutational processes in human somatic cells

A fundamental question in neuroscience concerns the relation between the spiking of individual neurons and the aggregate electrical activity of neuronal ensembles as seen in local field potentials (LFPs). Because LFPs reflect both spiking activity and subthreshold events, this question is not simply one of data aggregation. Recording from 20 neurosurgical patients, we directly examined the relation between LFPs and neuronal spiking. Examining 2030 neurons in widespread brain regions, we found that firing rates were positively correlated with broadband (2-150 Hz) shifts in the LFP power spectrum. In contrast, narrowband oscillations correlated both positively and negatively with firing rates at different recording sites. Broadband power shifts were a more reliable predictor of neuronal spiking than narrowband power shifts. These findings suggest that broadband LFP power provides valuable information concerning neuronal activity beyond that contained in narrowband oscillations.

https://www.jneurosci.org/content/jneuro/29/43/13613.full.pdf

Broadband Shifts in Local Field Potential Power Spectra Are Correlated with Single-Neuron Spiking in Humans

The rapid development of the theory of robust estimation (Huber, 1973) has created a need for computational procedures to produce robust estimates. We will review a number of different computational approaches for robust linear regression but focus on one—iteratively reweighted least-squares (IRLS). The weight functions that we discuss are a part of a semi-portable subroutine library called ROSEPACK (RObust Statistical Estimation PACKage) that has been developed by the authors and Virginia Klema at the Computer Research Center of the National Bureau of Economic Research, Inc. in Cambridge, Mass. with the support of the National Science Foundation. This library (Klema, 1976) makes it relatively simple to implement an IRLS regression package.

Robust regression using iteratively reweighted least-squares

In recent years, graphics has become an essential part of modern data analysis It is particularly useful for interactive data analysis This paper describes a system called CLOUDS which is designed to make available on inexpensive storage tube terminals a wide range of graphic tools related to data analysis, economics, and management science The system can be accessed nationwide by non profit organizations via the National Bureau of Economic Research computer network

/pdf/graphics-for-data-analysis-49bbcpkjhr.pdf

Roy E. Welsch

Papers

Robust regression using iteratively reweighted least-squares

Graphics for data analysis