Wavelet-based denoising for 3D OCT images

Optical coherence tomography produces high resolution medical images based on spatial and temporal coherence of the optical waves backscattered from the scanned tissue. However, the same coherence introduces speckle noise as well; this degrades the quality of acquired images. In this paper we propose a technique for noise reduction of 3D OCT images, where the 3D volume is considered as a sequence of 2D images, i.e., 2D slices in depth-lateral projection plane. In the proposed method we first perform recursive temporal filtering through the estimated motion trajectory between the 2D slices using noise-robust motion estimation/compensation scheme previously proposed for video denoising. The temporal filtering scheme reduces the noise level and adapts the motion compensation on it. Subsequently, we apply a spatial filter for speckle reduction in order to remove the remainder of noise in the 2D slices. In this scheme the spatial (2D) speckle-nature of noise in OCT is modeled and used for spatially adaptive denoising. Both the temporal and the spatial filter are wavelet-based techniques, where for the temporal filter two resolution scales are used and for the spatial one four resolution scales. The evaluation of the proposed denoising approach is done on demodulated 3D OCT images on different sources and of different resolution. For optimizing the parameters for best denoising performance fantom OCT images were used. The denoising performance of the proposed method was measured in terms of SNR, edge sharpness preservation and contrast-to-noise ratio. A comparison was made to the state-of-the-art methods for noise reduction in 2D OCT images, where the proposed approach showed to be advantageous in terms of both objective and subjective quality measures

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Combined wavelet domain and motion compensated filtering compliant with video codecs

In this paper, we introduce the idea of using motion estimation resources from a video codec for video denoising. This is not straightforward because the motion estimators aimed for video compression and coding, tolerate errors in the estimated motion field and hence are not directly applicable to video denoising. To solve this problem, we propose a novel motion field filtering step that refines the accuracy of the motion estimates to a degree that is required for denoising. We illustrate the use of the proposed motion estimation method within a wavelet-based video denoising scheme. The resulting video denoising method is of low-complexity and receives comparable results with respect to the latest video denoising methods

Methods for detection and characterization of signals in noisy data with the Hilbert-Huang Transform

The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution but also renders it susceptible to degradation from noise. We show that complementing the HHT with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal to noise ratio.Comment: submitted to PRD, 10 pages, 9 figures in colo