Recovering Sparse Signals Using Sparse Measurement Matrices in Compressed DNA Microarrays

Abstract

Abstract-Microarrays (DNA, protein, etc.) are massively parallel affinity-based biosensors capable of detecting and quantifying a large number of different genomic particles simultaneously. Among them, DNA microarrays comprising tens of thousands of probe spots are currently being employed to test multitude of targets in a single experiment. In conventional microarrays, each spot contains a large number of copies of a single probe designed to capture a single target, and, hence, collects only a single data point. This is a wasteful use of the sensing resources in comparative DNA microarray experiments, where a test sample is measured relative to a reference sample. Typically, only a fraction of the total number of genes represented by the two samples is differentially expressed, and, thus, a vast number of probe spots may not provide any useful information. To this end, we propose an alternative design, the so-called compressed microarrays, wherein each spot contains copies of several different probes and the total number of spots is potentially much smaller than the number of targets being tested. Fewer spots directly translates to significantly lower costs due to cheaper array manufacturing, simpler image acquisition and processing, and smaller amount of genomic material needed for experiments. To recover signals from compressed microarray measurements, we leverage ideas from compressive sampling. For sparse measurement matrices, we propose an algorithm that has significantly lower computational complexity than the widely used linear-programming-based methods, and can also recover signals with less sparsity.

On recovery of block-sparse signals via mixed l 2 /l q (0 < q ≤ 1) norm minimization

“…Such block-sparse signals arise in various application problems, say, DNA microarrays [7,8], equalization of sparse communication channels [9], source localization [10], wideband spectrum sensing [11], and color imaging [12].…”

Block Sparse Signals Recovery via Block BacktrackingBased Matching Pursuit Method

“…The compressed sensing (CS) involves recovery of the unknown sparse signal from this linear system [1]: y = Φx, where x is an unknown signal of length N, Φ ∈ R M×N (M<N) is the measurement matrix, y denotes the observation vector of length M . This problem has been widely applied in sparse channel estimation [2] and remote spectral sensing [3]. Since M<N, it is ill-posed to reconstruct x given y.…”

SBL-based multi-task algorithms for recovering block-sparse signals with unknown partitions

“…If in addition to sparsity, the signal representation is also structured in the form of clustered non-zeros, the signal would be referred to as being block-sparse. In practice, block-sparsity can be found in multi-band signals [2] or in the measurements of gene expression levels [3]. It has been shown that exploring the block-sparsity enables robust signal recovery from fewer compressive measurements [4].…”