The Role of Redundant Bases and Shrinkage Functions in Image Denoising.

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image, in the transform domain, using a set of shrinkage functions (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used. For example, it is widely known that applying SFs in a redundant basis improves the results. However, it is barely known that the shape of the SFs should be changed when the transform used is redundant. In this paper, we introduce a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. We suggest three schemes for optimizing the SFs and provide bounds of the remaining noise, in each scheme, with respect to the other alternatives. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. Furthermore, for redundant bases, we provide the expected denoising gain that can be achieved, relative to the unitary basis, as a function of the redundancy rate.

Integrative genomic analysis by interoperation of bioinformatics tools in GenomeSpace.

Complex biomedical analyses require the use of multiple software tools in concert and remain challenging for much of the biomedical research community. We introduce GenomeSpace (http://www.genomespace.org), a cloud-based, cooperative community resource that currently supports the streamlined interaction of 20 bioinformatics tools and data resources. To facilitate integrative analysis by non-programmers, it offers a growing set of 'recipes', short workflows to guide investigators through high-utility analysis tasks.

Two DNA-encoded strategies for increasing expression with opposing effects on promoter dynamics and transcriptional noise.

Individual cells from a genetically identical population exhibit substantial variation in gene expression. A significant part of this variation is due to noise in the process of transcription that is intrinsic to each gene, and is determined by factors such as the rate with which the promoter transitions between transcriptionally active and inactive states, and the number of transcripts produced during the active state. However, we have a limited understanding of how the DNA sequence affects such promoter dynamics. Here, we used single-cell time-lapse microscopy to compare the effect on transcriptional dynamics of two distinct types of sequence changes in the promoter that can each increase the mean expression of a cell population by similar amounts but through different mechanisms. We show that increasing expression by strengthening a transcription factor binding site results in slower promoter dynamics and higher noise as compared with increasing expression by adding nucleosome-disfavoring sequences. Our results suggest that when achieving the same mean expression, the strategy of using stronger binding sites results in a larger number of transcripts produced from the active state, whereas the strategy of adding nucleosome-disfavoring sequences results in a higher frequency of promoter transitions between active and inactive states. In the latter strategy, this increased sampling of the active state likely reduces the expression variability of the cell population. Our study thus demonstrates the effect of cis-regulatory elements on expression variability and points to concrete types of sequence changes that may allow partial decoupling of expression level and noise.

The gray-code filter kernels.

In this paper, we introduce a family of filter kernels--the Gray-Code Kernels (GCK) and demonstrate their use in image analysis. Filtering an image with a sequence of Gray-Code Kernels is highly efficient and requires only two operations per pixel for each filter kernel, independent of the size or dimension of the kernel. We show that the family of kernels is large and includes the Walsh-Hadamard kernels, among others. The GCK can be used to approximate any desired kernel and, as such forms, a complete representation. The efficiency of computation using a sequence of GCK filters can be exploited for various real-time applications, such as, pattern detection, feature extraction, texture analysis, texture synthesis, and more.