Universal Minimax Discrete Denoising under Channel Uncertainty

The goal of a denoising algorithm is to recover a signal from its noise-corrupted observations. Perfect recovery is seldom possible and performance is measured under a given single-letter fidelity criterion. For discrete signals corrupted by a known discrete memoryless channel, the DUDE was recently shown to perform this task asymptotically optimally, without knowledge of the statistical properties of the source. In the present work we address the scenario where, in addition to the lack of knowledge of the source statistics, there is also uncertainty in the channel characteristics. We propose a family of discrete denoisers and establish their asymptotic optimality under a minimax performance criterion which we argue is appropriate for this setting. As we show elsewhere, the proposed schemes can also be implemented computationally efficiently.Comment: Submitted to IEEE Transactions of Information Theor

Informatics Enhanced SNP Microarray Analysis of 30 Miscarriage Samples Compared to Routine Cytogenetics

Purpose: The metaphase karyotype is often used as a diagnostic tool in the setting of early miscarriage; however this technique has several limitations. We evaluate a new technique for karyotyping that uses single nucleotide polymorphism microarrays (SNP). This technique was compared in a blinded, prospective fashion, to the traditional metaphase karyotype. Methods: Patients undergoing dilation and curettage for first trimester miscarriage between February and August 2010 were enrolled. Samples of chorionic villi were equally divided and sent for microarray testing in parallel with routine cytogenetic testing. Results: Thirty samples were analyzed, with only four discordant results. Discordant results occurred when the entire genome was duplicated or when a balanced rearrangement was present. Cytogenetic karyotyping took an average of 29 days while microarray-based karytoyping took an average of 12 days. Conclusions: Molecular karyotyping of POC after missed abortion using SNP microarray analysis allows for the ability to detect maternal cell contamination and provides rapid results with good concordance to standard cytogenetic analysis

Algorithms for discrete denoising under channel uncertainty,” Submitted to

The goal of a denoising algorithm is to reconstruct a signal from its noise-corrupted observations. Perfect reconstruction is seldom possible and performance is measured under a given fidelity criterion. In a recent work, the authors addressed the problem of denoising unknown discrete signals corrupted by a discrete memoryless channel when the channel, rather than being completely known, is only known to lie in some uncertainty set of possible channels. A (sequence of) denoiser(s) was derived for this case and shown to be asymptotically optimal with respect to a worst-case criterion argued most relevant to this setting. In the present work we address the implementation and complexity of this denoiser, establishing its practicality. We also present empirical results suggesting the potential of these schemes to do well in practice. A key component of our schemes is an estimator of the subset of channels in the uncertainty set that are feasible in the sense of giving rise to the noisy signal statistics for some noiseless signal distribution. We establish the efficiency of this estimator (theoretically, algorithmically, and experimentally). We also present a modification of the recently developed discrete universal denoiser (DUDE) that assumes a channel based on the said estimator, and show that, in practice, the resulting scheme often performs comparably to our asymptotically minimax schemes. For concreteness, we focus on the binary alphabet case, but also discuss the extensions of the algorithms to general finite alphabets. Index Terms Channel Uncertainty, convex optimization, denoising algorithms, discrete universal denoising, image denoising, minimax schemes. I

Non-invasive prenatal detection of trisomy 13 using a single nucleotide polymorphism- and informatics-based approach.

PURPOSE:To determine how a single nucleotide polymorphism (SNP)- and informatics-based non-invasive prenatal aneuploidy test performs in detecting trisomy 13. METHODS:Seventeen trisomy 13 and 51 age-matched euploid samples, randomly selected from a larger cohort, were analyzed. Cell-free DNA was isolated from maternal plasma, amplified in a single multiplex polymerase chain reaction assay that interrogated 19,488 SNPs covering chromosomes 13, 18, 21, X, and Y, and sequenced. Analysis and copy number identification involved a Bayesian-based maximum likelihood statistical method that generated chromosome- and sample-specific calculated accuracies. RESULTS:Of the samples that passed a stringent DNA quality threshold (94.1%), the algorithm correctly identified 15/15 trisomy 13 and 49/49 euploid samples, for 320/320 correct copy number calls. CONCLUSIONS:This informatics- and SNP-based method accurately detects trisomy 13-affected fetuses non-invasively and with high calculated accuracy