2 research outputs found
Residual Ratio Thresholding for Model Order Selection
Model order selection (MOS) in linear regression models is a widely studied
problem in signal processing. Techniques based on information theoretic
criteria (ITC) are algorithms of choice in MOS problems. This article proposes
a novel technique called residual ratio thresholding for MOS in linear
regression models which is fundamentally different from the ITC based MOS
criteria widely discussed in literature. This article also provides a rigorous
mathematical analysis of the high signal to noise ratio (SNR) and large sample
size behaviour of RRT. RRT is numerically shown to deliver a highly competitive
performance when compared to popular model order selection criteria like Akaike
information criterion (AIC), Bayesian information criterion (BIC), penalised
adaptive likelihood (PAL) etc. especially when the sample size is small.Comment: 13 pages, 23 figure
High SNR Consistent Compressive Sensing Without Signal and Noise Statistics
Recovering the support of sparse vectors in underdetermined linear regression
models, \textit{aka}, compressive sensing is important in many signal
processing applications. High SNR consistency (HSC), i.e., the ability of a
support recovery technique to correctly identify the support with increasing
signal to noise ratio (SNR) is an increasingly popular criterion to qualify the
high SNR optimality of support recovery techniques. The HSC results available
in literature for support recovery techniques applicable to underdetermined
linear regression models like least absolute shrinkage and selection operator
(LASSO), orthogonal matching pursuit (OMP) etc. assume \textit{a priori}
knowledge of noise variance or signal sparsity. However, both these parameters
are unavailable in most practical applications. Further, it is extremely
difficult to estimate noise variance or signal sparsity in underdetermined
regression models. This limits the utility of existing HSC results. In this
article, we propose two techniques, \textit{viz.}, residual ratio minimization
(RRM) and residual ratio thresholding with adaptation (RRTA) to operate OMP
algorithm without the \textit{a priroi} knowledge of noise variance and signal
sparsity and establish their HSC analytically and numerically. To the best of
our knowledge, these are the first and only noise statistics oblivious
algorithms to report HSC in underdetermined regression models.Comment: 13 pages, 6 figure