A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency
representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional
Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner
distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive
type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive
sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform
domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction
algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted
by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal
representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases
of monocomponent and multicomponent signals.
Robust signal analysis based on the L-statistic was introduced for signals disturbed with high additive impulse noise.
The basic idea is that a certain, usually large number of arbitrary positioned signal samples is declared as heavily
corrupted by noise. Then, these samples are removed. Thus, they can be considered as absent or unavailable. Hence, the
L-statistics significantly reduces the number of available signal samples. Moreover these samples are randomly
distributed, so an efficient analysis of such signals invokes the compressive sensing reconstruction algorithms. Also, it
will be shown that the variance of noise, produced by missing samples, can be used as powerful tool for signal
reconstruction. Additionally, in order to provide separation of stationary and nonstationary signals the L-statistic is
combined with compressive sensing algorithms. The theoretical considerations are verified by various examples, where
discrete forms of the Fourier transform and short-time Fourier transform are used to demonstrate the effective integration
of the two techniques.
An image watermarking scheme that combines Hermite functions expansion and space/spatial-frequency analysis is proposed. In the first step, the Hermite functions expansion is employed to select busy regions for watermark embedding. In the second step, the space/spatial-frequency representation and Hermite functions expansion are combined to design the imperceptible watermark, using the host local frequency content. The Hermite expansion has been done by using the fast Hermite projection method. Recursive realization of Hermite functions significantly speeds up the algorithms for regions selection and watermark design. The watermark detection is performed within the space/spatial-frequency domain. The detection performance is increased due to the high information redundancy in that domain in comparison with the space or frequency domains, respectively. The performance of the proposed procedure has been tested experimentally for different watermark strengths, i.e., for different values of the peak signal-to-noise ratio (PSNR). The proposed approach provides high detection performance even for high PSNR values. It offers a good compromise between detection performance (including the robustness to a wide variety of common attacks) and imperceptibility.
A new procedure for watermarking in the 8×8 block-based discrete cosine transform (DCT) domain (used for JPEG compression) is proposed. The influence of JPEG quantization on watermarked coefficients and on watermark is considered. The criterion for coefficients selection is derived, providing robustness for an arbitrary quantization degree. The modified form of coefficients probability density function (pdf) leads to the class of modified optimal detectors. Theoretical results are illustrated on various examples. Efficiency of the proposed procedure is shown in the presence of different quantization degrees, and other common attacks.