On the detection of low rank matrices in the high-dimensional regime. Chevreuil, A. & Loubaton, P. In *2018 26th European Signal Processing Conference (EUSIPCO)*, pages 1102-1106, Sep., 2018.

Paper doi abstract bibtex

Paper doi abstract bibtex

We address the detection of a low rank n×n matrix X0 from the noisy observation X0+Z when n → ∞, where Z is a complex Gaussian random matrix with independent identically distributed ℕc (0, [1/n]) entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value λ1(X0) of X0 verifies λ1(X0) > 1, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition λ1(X0) <; 1, there are no consistent tests. Our proof is inspired by previous works devoted to the case of rank 1 matrices X0.

@InProceedings{8553606, author = {A. Chevreuil and P. Loubaton}, booktitle = {2018 26th European Signal Processing Conference (EUSIPCO)}, title = {On the detection of low rank matrices in the high-dimensional regime}, year = {2018}, pages = {1102-1106}, abstract = {We address the detection of a low rank n×n matrix X0 from the noisy observation X0+Z when n → ∞, where Z is a complex Gaussian random matrix with independent identically distributed ℕc (0, [1/n]) entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value λ1(X0) of X0 verifies λ1(X0) > 1, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition λ1(X0) <; 1, there are no consistent tests. Our proof is inspired by previous works devoted to the case of rank 1 matrices X0.}, keywords = {matrix algebra;random processes;low rank matrices;high-dimensional regime;consistent tests;singular value;gaussian random matrix;noisy observation;Tensile stress;Upper bound;Europe;Signal processing;Random variables;Matrix decomposition;Noise measurement;statistical detection tests;large random matrices;large deviation principle}, doi = {10.23919/EUSIPCO.2018.8553606}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2018/papers/1570437336.pdf}, }

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