Signals with time-varying frequency content are generally best represented in the time frequency (TF) domain, with the components instantaneous frequency laws being their key nonstationary features. There are a number of methods for TF distribution calculation (TFD), however, most of them add unwanted artifacts, making the TFD interpretation more difficult. In this paper, we use a compressive sensing approach to suppress or completely eliminate those artifacts. Furthermore, a basis pursuit algorithm is employed for signal reconstruction in order to reduce resolution loss, which is a mayor obstacle of existing TFD design methods.

This study proposes an adaptive method for components instantaneous frequency (IF) estimation of noisy non‐stationary multicomponent signals, combined with the components time‐support estimation method based on the short‐time Rényi entropy (STRE). Components localisation and separation are done using a double‐direction component tracking and extraction method presented here, while the IF estimation is done using the adaptive algorithms based on the intersection of confidence intervals (ICI) rule and the relative intersection of confidence intervals (RICI) rule. The results obtained using the ICI and RICI rules are compared for various window types, signal‐to‐noise ratios and time–frequency distributions, both with and without using the information on components time support. Most of the errors in IF estimation using the ICI and RICI‐based methods are caused by imprecise components time‐support estimation. The proposed methods combined with the STRE have achieved a significant accuracy improvement in terms of the mean absolute error and the mean squared error, reducing them by up to 73 and 93%, respectively. The method has been applied to real‐life signals and proven to be an efficient tool for IF estimation of noisy non‐stationary multicomponent signals.

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

A method for the instantaneous frequency (IF) estimation of a monocomponent nonlinear frequency modulated (FM) signal based on the pseudo Wigner-Ville distribution (PWVD) with an adaptive window width is presented. In order to improve the IF estimation accuracy, the original sliding pair-wise intersection of confidence intervals (SPICI) rule has been modified. An additional criterion for a proper window width selection is introduced, which takes into account the amount of overlap between the current and the previous confidence interval relative to the current interval length. The presented results show that the proposed method outperforms the original SPICI-based method by up to 42% in terms of the mean absolute error and up to 73% in terms of the mean squared error. It is also less sensitive to the window widths set selection than the original method.

In this letter, we have proposed a signal denoising method based on a modification of the intersection of confidence intervals (ICI) rule. The ICI rule is complemented by the relative intersection of confidence intervals length which is used as an additional criterion for adaptive filter support selection. It is shown that the proposed method outperforms the original ICI method equipped with the local polynomial approximation (LPA), as well as various conventional wavelet shrinkage methods.

Selecting a time-frequency distribution (TFD) which represents a signal in an optimal way is commonly done by visually comparing plots of different TFD. This paper presents a procedure that allows the analyst to perform the same task in an automatic way. Using the resolution performance measure for TFD, the procedure optimises all distributions considered and selects the one which results into best concentration of signal components around their instantaneous frequency laws, as well as best suppression of the interference terms in the time-frequency plane. To do this requires us to define a methodology to measure the time-frequency characteristics of a signal from its optimal TFD. An algorithm which implements this methodology is described and results are presented.