Lasith Adhikari

Nonconvex relaxation for Poisson intensity reconstruction

Critical to accurate reconstruction of sparse signals from low-dimensional Poisson observations is the solution of nonlinear optimization problems that promote sparse solutions. Theoretically, non-convex ℓp-norm minimization (0 ≤ p <; 1) would lead to more accurate reconstruction than the convex ℓ1-norm relaxation commonly used in sparse signal recovery. In this paper, we propose an extension to the existing SPIRAL-ℓ1 algorithm based on the Generalized Soft-Thersholding (GST) function to better recover signals with mostly nonzero entries from Poisson observations. This approach is based on iteratively minimizing a sequence of separable subproblems of the nonnegatively constrained, ℓp-penalized negative Poisson log-likelihood objective function using the GST function. We demonstrate the effectiveness of the proposed method, called SPIRAL-ℓp, through numerical experiments.

Sparse signal recovery methods for variant detection in next-generation sequencing data

Recent advances in high-throughput sequencing technologies, have led to the collection of vast quantities of genomic data., Structural variants (SVs) - rearrangements of the genome, larger than one letter such as inversions, insertions, deletions, and duplications - are an important source of genetic, variation and have been implicated in some genetic diseases., However, inferring SVs from sequencing data has proven to, be challenging because true SVs are rare and are prone to, low-coverage noise. In this paper, we attempt to mitigate the, deleterious effects of low-coverage sequences by following a, maximum likelihood approach to SV prediction. Specifically, we model the noise using Poisson statistics and constrain, the solution with a sparsity-promoting ℓ1 penalty since SV, instances should be rare. In addition, because offspring SVs, inherit SVs from their parents, we incorporate familial relationships, in the optimization problem formulation to increase, the likelihood of detecting true SV occurrences. Numerical, results are presented to validate our proposed approach.

Analysis of p-norm regularized subproblem minimization for sparse photon-limited image recovery

Critical to accurate reconstruction of sparse signals from low-dimensional low-photon count observations is the solution of nonlinear optimization problems that promote sparse solutions. In this paper, we explore recovering high-resolution sparse signals from low-resolution measurements corrupted by Poisson noise using a gradient-based optimization approach with non-convex regularization. In particular, we analyze zero-finding methods for solving the p-norm regularized minimization subproblems arising from a sequential quadratic approach. Numerical results from fluorescence molecular tomography are presented.

Constrained variant detection with SPaRC: Sparsity, parental relatedness, and coverage

Structural variants (SVs) are rearrangements of DNA sequences such as inversions, deletions, insertions and translocations. The common method for detecting SVs has been to sequence data from a test genome and map it to a reference genome. More recently, DNA sequencing studies may consist of hundreds, or even thousands of individuals, some of which may be related. In order to improve our ability to identify SVs, we boost the true SV signals by simultaneously analyzing parent and child genomes. Our algorithmic formulation - SPaRC - employs realistic criteria such as sparsity of SVs, relatedness between individuals and variable sequencing coverage throughout the genome.Structural variants (SVs) are rearrangements of DNA sequences such as inversions, deletions, insertions and translocations. The common method for detecting SVs has been to sequence data from a test genome and map it to a reference genome. More recently, DNA sequencing studies may consist of hundreds, or even thousands of individuals, some of which may be related. In order to improve our ability to identify SVs, we boost the true SV signals by simultaneously analyzing parent and child genomes. Our algorithmic formulation - SPaRC - employs realistic criteria such as sparsity of SVs, relatedness between individuals and variable sequencing coverage throughout the genome.

Limited-memory trust-region methods for sparse relaxation

In this paper, we solve the ℓ2-ℓ1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and applying a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving computational time.

Biomedical signal recovery: Genomic variant detection in family lineages

Structural variations (SVs) — genomic rearrangements such as insertions, deletions and duplications — represent an important class of genomic variation. These mutations have been associated with both genetic diseases (e.g., cancer) and promoting genetic diversity. The common approach to detecting SVs in an unknown genome involves sequencing fragments of the genome, comparing them to a reference genome, and predicting SVs based on identified discordant fragments. However, detecting SVs from traditional DNA sequencing is challenging due to the presence of errors and biases in the DNA sequencing process as well as problems aligning sequences to a reference genome. The majority of existing methods use hierarchical relationships to detect these genetic changes, but often post-process this information. Our work aims to improve on existing SV detection methods in three ways: First, we use a continuous relaxation of admissible solutions to apply gradient-based optimization techniques. Second, since SVs are rare, we incorporate an l\ sparsity-promoting penalty term. Third, we improve on our previous work by using a block-coordinate descent approach to predict variants in families of individuals. We demonstrate the effectiveness of our method on a variety of simulated datasets and real genomes of a two parent-two child family.

Sparse diploid spatial biosignal recovery for genomic variation detection

Structural variants (SVs) - such as duplications, deletions and inversions - are rearrangements of an individuals genome relative to a given reference. The common method for detection of SVs is to sequence fragments from an individuals genome, map them to the appropriate reference and, by identifying discordant mappings, predict the locations and type of SV. However, errors in both the sequencing and mapping process will result in signals that look like SVs, resulting in inaccurate predictions. In addition, because of variation in sequencing coverage even when the evidence of an SV is present, determining if an individual has the SV present on one or both of their chromosomes is challenging. In our work, we seek to improve upon standard methods for SV detection in three ways. First, to reduce false-positive predictions, we simultaneously predict SVs in a parent and child using properties of inheritance to constrain the space of possible SVs. Second, we predict if a variant is homozygous (SV is on two chromosomes) or heterozygous (SV is on one chromosome). Third, we utilize a gradient-based optimization approach and constrain our solution with a sparsity-promoting ℓ1 penalty (since SV instances should be rare). We demonstrate the improved performance of our computational approach on both simulated genomes as well as a parent-child trio from the 1000 Genomes Project.

Nonconvex regularization for sparse genomic variant signal detection

Recent research suggests an overwhelming proportion of humans have genomic structural variants (SVs): rearrangements of regions in the genome such as inversions, insertions, deletions and duplications. The standard approach to detecting SVs in an unknown genome involves sequencing paired-reads from the genome in question, mapping them to a reference genome, and analyzing the resulting configuration of fragments for evidence of rearrangements. Because SVs occur relatively infrequently in the human genome, and erroneous read-mappings may suggest the presence of an SV, approaches to SV detection typically suffer from high false-positive rates. Our approach aims to more accurately distinguish true from false SVs in two ways: First, we solve a constrained optimization equation consisting of a negative Poisson log-likelihood objective function with an additive penalty term that promotes sparsity. Second, we analyze multiple related individuals simultaneously and enforce familial constraints. That is, we require any SVs predicted in children to be present in one of their parents. Our problem formulation decreases the false positive rate despite a large amount of error from both DNA sequencing and mapping. By incorporating additional information, we improve our model formulation and increase the accuracy of SV prediction methods.

Non-convex Shannon entropy for photon-limited imaging

Reconstructing high-dimensional sparse signals from low-dimensional low-count photon observations is a challenging nonlinear optimization problem. In this paper, we build upon previous work on minimizing the Poisson log-likelihood and incorporate recent work on the generalized nonconvex Shannon entropy function for promoting sparsity in solutions. We explore the effectiveness of the proposed approach using numerical experiments.

Bounded sparse photon-limited image recovery

In photon-limited image reconstruction, the behavior of noise at the detector end is more accurately modeled as a Poisson point process than the common choice of a Gaussian distribution. As such, to recover the original signal more accurately, a penalized negative Poisson log-likelihood function - and not a least-squares function - is minimized. In many applications, including medical imaging, additional information on the signal of interest is often available. Specifically, its maximum and minimum amplitudes might be known a priori. This paper describes an approach that incorporates this information into a sparse photon-limited recovery method by the inclusion of upper and lower bound constraints. We demonstrate the effectiveness of the proposed approach on two different low-light deblurring examples.