Ana Sović

Efficient Least Absolute Deviation Adaptive Wavelet Filter Bank

Compact representation of signals and images is a key for many applications. Compactness is often achieved through linear transforms with good energy concentration property. We present an adaptive wavelet filter bank with fixed number of vanishing moments, plus additional local adaptation. Proposed adaptation method is conducted at each sample according to the least absolute deviation (LAD) criterion. Fixed vanishing moments provide for polynomial annihilation. Adaptation is aimed to achieve maximum sparseness for a wider class of signals, such as sine waves. LAD criterion results in more accurate adaptation on sudden changes of signal statistics. In this paper, an efficient LAD realization is proposed, in spite of nonexistence of the closed form solution. Combining least squares and LAD criterion, we have achieved unbiased adaptation, robust to noise. Due to its simplicity and acceptable computational speed, the proposed scheme is a good candidate for the real-world applications. In this paper, advantages of the proposed scheme are shown in signal denoising and reconstruction.

Restoration of soft x-ray laser images of nanostructures

We present advanced techniques for the restoration of images obtained by soft x-ray laser microscopy. We show two methods. One method is based on adaptive thresholding, while the other uses local Wiener filtering in the wavelet domain to achieve high noise gains. These wavelet based denoising techniques are improved using spatial noise modeling. The accurate noise model is built up from two consecutive images of the object and respective background images. To our knowledge, the results of both proposed approaches over-perform competitive methods. The analysis is robust to enable image acquisition with significantly lower exposure times, which is critical in samples that are sensitive to radiation damage as is the case of biological samples imaged by SXR microscopy.

A robust separable image denoising based on relative intersection of confidence intervals rule

Many microscopy images, or 3D depth maps can be represented using piecewise constant models. They usually contain noise due to sensor imperfectness. In this paper, an improved separable denoising method based on the relative intersection of confidence intervals rule is proposed. The method uses median averaging and is robust to outliers and different noise distributions. It over-performs competitive methods in the sense of edge preservation.

Directional image denoising method based on the relative intersection of confidence intervals rule

In this paper, the relative intersection of confidence intervals (ICI) rule is used to adaptively determine window sizes around each observed point in purpose of denoising. The relative ICI rule defines neighbourhoods of similar statistical properties for every signal sample. If we calculate a mean value on each window, it corresponds to the zero-order estimation and results in a denoised signal. Furthermore, the mean value can be replaced by median for additional robustness of estimation. The same approach could be taken on images. In this paper, we find the maximum window length in four, eight or sixteen directions around each pixel. Mean or median value of chosen surrounding pixels results in a denoised estimation of each observed pixel. The proposed denoising method was tested on an example of a piecewise constant image and compared to known methods. Under the given conditions, it has shown improvement in terms of the PSNR, MAE and subjective visual impression.