Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Review
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Bioinformatics
Compressed sensing with probabilistic measurements: a group testing solution
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
IEEE Transactions on Information Theory - Special issue on information theory in molecular biology and neuroscience
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Boolean Compressed Sensing and Noisy Group Testing
IEEE Transactions on Information Theory
On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
SIAM Journal on Matrix Analysis and Applications
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Group testing, also known as pooling, is a common technique used in high-throughput experiments in molecular biology to significantly reduce the number of tests required to identify rare biological interactions while correcting for experimental noise. Central to the group testing problem are 1) a pooling design that lays out how items are grouped together into pools for testing and 2) a decoder that interprets the results of the tested pools, identifying the active compounds. In this work, we take advantage of decoder guarantees from the field of compressed sensing (CS) to address the problem of efficient and reliable detection of biological interaction in noisy high-throughput experiments. We also use efficient combinatorial algorithms from group testing as well as established measurement matrices from CS to create pooling designs. First, we formulate the group testing problem in terms of a Boolean CS framework. We then propose a low-complexity $(l_1)$-norm decoder to interpret pooling test results and identify active compounds. We demonstrate the robustness of the proposed $(l_1)$-norm decoder in simulated experiments with false-positive and false-negative error rates typical of high-throughput experiments. When benchmarked against the current state-of-the-art methods, the proposed $(l_1)$-norm decoder provides superior error correction for the majority of the cases considered while being notably faster computationally. Additionally, we test the performance of the $(l_1)$-norm decoder against a real experimental data set, where 12,675 prey proteins were screened against 12 bait proteins. Lastly, we study the impact of different sparse pooling design matrices on decoder performance and show that the shifted transversal design (STD) is the most suitable among the pooling designs surveyed for biological applications of CS.