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We propose a frame-based representation of k-mers for detecting sequencingerrors and rare variants in next generation sequencing data obtained frompopulations of closely related genomes. Frames are sets of non-orthogonal basisfunctions, traditionally used in signal processing for noise removal. We definea frame for genomes and sequenced reads to consist of discrete spatial signalsof every k-mer of a given size. We show that each k-mer in the sequenced datacan be projected onto multiple frames and these projections are maximized forspatial signals corresponding to the k-mer's substrings. Our proposedclassifier, MultiRes, is trained on the projections of k-mers as features usedfor marking k-mers as erroneous or true variations in the genome. We evaluateMultiRes on simulated and real viral population datasets and compare it toother error correction methods known in the literature. MultiRes has 4 to 500times less false positives k-mer predictions compared to other methods,essential for accurate estimation of viral population diversity and theirde-novo assembly. It has high recall of the true k-mers, comparable to othererror correction methods. MultiRes also has greater than 95% recall fordetecting single nucleotide polymorphisms (SNPs), fewer false positive SNPs,while detecting higher number of rare variants compared to other variantcalling methods for viral populations. The software is freely available fromthe GitHub link (https://github.com/raunaq-m/MultiRes).

A frame-based representation of genomic sequences for removing errors and rare variant detection in NGS data