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Multiscale higher-order TV operators for L1 regularization.

ABSTRACT: In the realm of signal and image denoising and reconstruction, ?1 regularization techniques have generated a great deal of attention with a multitude of variants. In this work, we demonstrate that the ?1 formulation can sometimes result in undesirable artifacts that are inconsistent with desired sparsity promoting ?0 properties that the ?1 formulation is intended to approximate. With this as our motivation, we develop a multiscale higher-order total variation (MHOTV) approach, which we show is related to the use of multiscale Daubechies wavelets. The relationship of higher-order regularization methods with wavelets, which we believe has generally gone unrecognized, is shown to hold in several numerical results, although notable improvements are seen with our approach over both wavelets and classical HOTV. These results are presented for 1D signals and 2D images, and we include several examples that highlight the potential of our approach for improving two- and three-dimensional electron microscopy imaging. In the development approach, we construct the tools necessary for MHOTV computations to be performed efficiently, via operator decomposition and alternatively converting the problem into Fourier space.

SUBMITTER: Sanders T

PROVIDER: S-EPMC6208801 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Multiscale higher-order TV operators for L1 regularization.

Sanders Toby T Platte Rodrigo B RB

Advanced structural and chemical imaging 20181023 1

In the realm of signal and image denoising and reconstruction, ℓ 1 regularization techniques have generated a great deal of attention with a multitude of variants. In this work, we demonstrate that the ℓ 1 formulation can sometimes result in undesirable artifacts that are inconsistent with desired sparsity promoting ℓ 0 properties that the ℓ 1 formulation is intended to approximate. With this as our motivation, we develop a multiscale higher-order total variation (MHOTV) approach, which we s ...[more]

PMID: 30416939

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Project description:It is increasingly being recognized that physical interactions between distant chromosomal loci influence the expressivity of the genome. Thus, multiple enhancers may converge on a single gene promoter 1,2 and a single enhancer can stochastically loop to multiple promoters 3. Regulatory elements from neighboring domains or from other chromosomes may interact to generate chromatin structures poised for transcription4-8 or repression 9-11. However, a broader perspective on the formation and function of such networks remains largely unexplored. Using the high-resolution 4C (Circular Chromosome Conformation Capture) analysis, we identify here a genome-wide physical network between genomically imprinted domains impinging H19 imprinting control region (ICR). Sequences interacting with the H19 ICR constitutively map at or within most of known imprinted domains both in mouse embryonic stem cells and in vitro-derived embryoid bodies, despite distinct differences in chromatin environments. Moreover, all-to-all 3D DNA FISH analyses revealed that imprinted domains from 7 different chromosomes co-localize with each other in pair-wise patterns, highlighting the dynamic nature of these interactions. The observed interaction network is dependent on CTCF binding sites within the maternally inherited H19 ICR allele and delays reprogramming of epigenetic features at imprinted domains during male germline development. As other imprinted regions can interact with each other in an H19 ICR-dependent manner, the H19 ICR emerges as an organizer of chromosomal networks by specifically recognizing and reconfiguring imprinted domains. We propose that an ancient key regulatory region, such as the H19 ICR, gradually impacted epigenetic modifications via long-range interactions in the germline to facilitate the recruitment of imprinted genes and their formation in clusters during mammalian radiation. Furthermore, the perspective of epigenetic lesions de-stabilizing such chromosomal networks may advance our understanding of how quantitative traits influence human diseases, such as cancer.

Dataset Information

Multiscale higher-order TV operators for L1 regularization.

Publications

Multiscale higher-order TV operators for L1 regularization.

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