Optical Coherence Tomography (OCT) images, as well as a majority of medical images, are imposed to speckle noise while capturing. Since the quality of these images is crucial for detecting any abnormalities, we develop an improved denoising algorithm that is particularly appropriate for OCT images. The essential idea is to combine two non-dataadaptive transform-based denoising methods that are capable to preserve different important structures appearing in OCT images while providing a very good denoising performance. Based on our numerical experiments, the most appropriate non-data-adaptive transforms for denoising and feature extraction are the Discrete Cosine Transform (DCT) (capturing local patterns) and the Dual-Tree Complex Wavelet Transform (DTCWT) (capturing piecewise smooth image features). These two transforms are combined using the Dual Basis Pursuit Denoising (DBPD) algorithm. Further improvement of the denoising procedure is achieved by total variation (TV) regularization and by employing an iterative algorithm based on DBPD.

In this paper we introduce two algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real positive frequency parameters and therefore strongly generalizes usual Fourier sums. The proposed methods both employ a set of equidistant signal values as input data. The ESPRIT method for cosine sums is a Prony-like method and applies matrix pencils of Toeplitz + Hankel matrices while the ESPIRA method is based on rational approximation of DCT data and can be understood as a matrix pencil method for special Loewner matrices. Compared to known numerical methods for recovery of exponential sums, the design of the considered new algorithms directly exploits the special real structure of the signal model and therefore usually provides real parameter estimates for noisy input data, while the known general recovery algorithms for complex exponential sums tend to yield complex parameters in this case.

In this paper we introduce two new algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real positive frequency parameters and therefore strongly generalizes usual Fourier sums. The proposed methods both employ a set of equidistant signal values as input data. The ESPRIT method for cosine sums is a Prony-like method and applies matrix pencils of Toeplitz + Hankel matrices while the ESPIRA method is based on rational approximation of DCT data and can be understood as a matrix pencil method for special Loewner matrices. Compared to known numerical methods for recovery of exponential sums, the design of the considered new algorithms directly exploits the special real structure of the signal model and therefore usually provides real parameter estimates for noisy input data, while the known general recovery algorithms for complex exponential sums tend to yield complex parameters in this case.