In this work we develop a general optimization framework to more accurately

recover structural variants (SVs) in low-coverage sequencing data from

genomes of related individuals. In previous work the framework incorporated

biological constraints that reflect relatedness between individuals and enforced

sparsity to model the rarity of SVs. This framework operated under the assumption

that the genomes were haploid, meaning that each individual had one

copy of the genetic material. There are two main contributions of this thesis:

First we propose an approach that allows the child signal to possess variants

that are not present in either parent (i.e., novel SVs) under the assumption of

haploid signals. Second, we propose an approach to reconstruct the signals of

two parents and a child under the assumption of diploid genomes. We tested

the e↵ectiveness of these approaches on both simulated data and data from the

1000 Genomes Project.