6 research outputs found
Deep Dictionary Learning: A PARametric NETwork Approach
Deep dictionary learning seeks multiple dictionaries at different image
scales to capture complementary coherent characteristics. We propose a method
for learning a hierarchy of synthesis dictionaries with an image classification
goal. The dictionaries and classification parameters are trained by a
classification objective, and the sparse features are extracted by reducing a
reconstruction loss in each layer. The reconstruction objectives in some sense
regularize the classification problem and inject source signal information in
the extracted features. The performance of the proposed hierarchical method
increases by adding more layers, which consequently makes this model easier to
tune and adapt. The proposed algorithm furthermore, shows remarkably lower
fooling rate in presence of adversarial perturbation. The validation of the
proposed approach is based on its classification performance using four
benchmark datasets and is compared to a CNN of similar size
Large System Analysis of Box-Relaxation in Correlated Massive MIMO Systems Under Imperfect CSI (Extended Version)
In this paper, we study the mean square error (MSE) and the bit error rate
(BER) performance of the box-relaxation decoder in massive
multiple-input-multiple-output (MIMO) systems under the assumptions of
imperfect channel state information (CSI) and receive-side channel correlation.
Our analysis assumes that the number of transmit and receive antennas (,and
) grow simultaneously large while their ratio remains fixed. For simplicity
of the analysis, we consider binary phase shift keying (BPSK) modulated
signals. The asymptotic approximations of the MSE and BER enable us to derive
the optimal power allocation scheme under MSE/BER minimization. Numerical
simulations suggest that the asymptotic approximations are accurate even for
small and . They also show the important role of the box constraint in
mitigating the so called double descent phenomenon
Precise error analysis of the LASSO
A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, k-sparse signal x0 ∈ n from underdetermined, noisy, linear measurements y = Ax0 + z ∈ m. One standard approach is to solve the following convex program x = arg minx y -Ax2+λx1, which is known as the ℓ2-LASSO. We assume that the entries of the sensing matrix A and of the noise vector z are i.i.d Gaussian with variances 1/m and σ2. In the large system limit when the problem dimensions grow to infinity, but in constant rates, we precisely characterize the limiting behavior of the normalized squared error x -x0 2 2/σ2. Our numerical illustrations validate our theoretical predictions