Squared-loss mutual information (SMI) is a surrogate of Shannon mutual information that is more advantageous for estimation. On the other hand, the coherence matrix of a pair of random vectors, a power-normalized version of the sample cross-covariance matrix, is a well-known second-order statistic found in the core of fundamental signal processing problems, such as canonical correlation analysis (CCA). This paper shows that SMI can be estimated from a pair of independent and identically distributed (i.i.d.) samples as a squared Frobenius norm of a coherence matrix estimated after mapping the data onto some fixed feature space. Moreover, low computation complexity is achieved through the fast Fourier transform (FFT) by exploiting the Toeplitz structure of the involved autocorrelation matrices in that space. The performance of the method is analyzed via computer simulations using Gaussian mixture models.

An information-theoretic approach is described to estimate the determinant of the covariance matrix of a random vector sequence (a common task in a wide range of estimation and detection problems in signal processing for communications). The method is based on a prior entropy-based processing of the data using kernels and offers robustness against small-entropy contamination. The trade-off between optimality, accuracy and robustness is analyzed, along with the impact of the relative kernel bandwidth and data size.

A novel independence test for continuous random sequences is proposed in this paper. The test is based on seeking for coherence in a particular fixed-dimension feature space based on a uniform sampling of the sample characteristic function of the data, providing significant computational advantages over kernel methods. This feature space relates uncorrelation and independence, allowing to analyze the second order statistics as it is encountered in traditional signal processing. As a result, the possibility of utilizing well known correlation tools arises, motivating the usage of Canonical Correlation Analysis as the main tool for detecting independence. Comparative simulation results are provided using a model based on fading AWGN channels.

Over the past decade, Multibeam Echosounders (MBES) have become one of the most used techniques in sea exploration. Modern MBES are capable of acquiring both bathymetric information on the seafloor and the reflectivity of the seafloor and water column. Water column imaging MBES surveys acquire significant amounts of data with rates that can exceed several GB/h depending on the ping rate. These large file sizes obtained from recording the full water column backscatter make remote transmission difficult if not prohibitive with current technology and bandwidth limitations. In this paper, we propose an algorithm to decorrelate water column and bathymetry data, focusing on the KMALL format released by Kongsberg Maritime in 2019. The pre-processing stage is integrated into FAPEC, a data compressor originally designed for space missions. Here, we test the algorithm with three different datasets: two of them provided by Kongsberg Maritime and one dataset from the Gulf of Mexico provided by Fugro USA Marine. We show that FAPEC achieves good compression ratios at high speeds using the pre-processing stage proposed in this paper. We also show the advantages of FAPEC over other lossless compressors as well as the quality of the reconstructed water column image after lossy compression at different levels. Lastly, we test the performance of the pre-processing stage, without the constraint of an entropy encoder, by means of the histograms of the original samples and the prediction errors.

We study the problem of estimating the overall mutual information in M independent parallel discrete-time memory-less Gaussian channels from N independent data sample pairs per channel (inputs and outputs). We focus on the case where the number of active channels L is sparse in comparison with the total number of channels (L M ), for which the direct application of the maximum likelihood principle is problematic due to overfitting, especially for moderate to small N . For this regime, we show that the bias of the mutual information estimate is reduced by resorting to the minimum description length (MDL) principle. As a result, simple pre-processing based on a perchannel threshold on the empirical squared correlation coefficient is required with a fixed threshold that monotonically decreases with N as 1 − N −1/N , for N ≥ 4. The resulting improvement is shown in terms of the estimated information bias.