## Image enhancement

*Andrey Nasonov, Alexey Lukin, Alexandra Nasonova, Andrey Krylov*

The problems of image and video resampling and multiframe superresolution are considered. They are posed as ill-posed inverse problems. Regularization methods based on Tikhonov regularization are used to solve there problems.

We also consider developing fast and low complexity edge-directional resizing algorithms for image and video.

A new technique to perform **edge sharpening** using grid warping is proposed. The idea of grid warping is to move the edge neighborhood pixels closer to the edge. The proposed algorithm is not posed as a global image deblurring method. It enhances only image edges neighborhood and practically does not affect image textures.

The proposed sharpening algorithm has the following features:

- It can be efficiently used as a post-processing method for global image deblurring methods
- No artifacts typical for traditional image deblurring methods like ringing effect or noise amplification are introduced, textures are preserved
- It does not need accurate PSF estimation
- Unlike morphological methods and shock filters, the resulting images look natural and do not inevitably become piecewise constant
- It can be used as a standalone method of image sharpening. It is a good choice in the presence of strong noise and complex and non-uniform blur kernel

The problem of development of fast rank algorithms for image enhancement is considered. Based on multiscale histograms and using lazy histogram updating technique we developed fast calculation scheme for finding

- Arbitrary rank element by neighborhood
- Mean by epsilon-V neighbourhood
- Mean by KNV neighbourhood
- Sliding equalization

## Image analysis

We consider the problem of evaluation of image enhancement algorithms like resampling, deringing, deblurring. The main idea is to find the areas where typical artifacts of image enhancement algorithms usually appear: blur and ringing artifacts.

The main idea is to find edges that are the most suitable for image quality analysis — the **basic edges**. The following constrains are imposed:

- These edges should be strong and distant from other edges to make possible to use them for blur and ringing level estimation
- These edges should survive after a certain level of high frequency degradation typical for blur, noise and ringing effects

Special metrics (BEP, BEN) are used to estimate the image quality in the neighborhood of the basic edges.

*Alexandra Nasonova, Andrey Krylov*

Development of edge width estimation algorithm is important for image enhancement and image quality analysis methods. We aim at developing an edge width estimation algorithm that is robust to image artifacts and noise.

*Andrey Nasonov, Andrey Krylov*

Ringing effect so known as Gibbs phenomenon in mathematical methods of image processing is the annoying effect in images and video appeared as rippling artifact near sharp edges. This effect is caused by distortion or loss of high frequency information in image. It can be found in images of different classes: MRI images, compressed images, oversharpened images, images transmitted over analog channel etc.

Our research on ringing effect has the following directions:

- Ringing effect detection
- Ringing effect suppression
- Development of the ringing database

Keypoints detection and local image descriptors construction is one of the basic problems in image analysis.

The keypoints detection and descriptors construction algorithms are based on Gauss-Laguerre circular harmonic functions (CHFs) image expansion. The interconnection between Gauss-Laguerre CHFs and 2D Hermite functions in conjunction with fast Hermite projection method is used to accelerate the computation.

The subjects of the current research are:

- Improvement of stability of Gauss-Laguerre keypoints descriptors to a class of projective and photometric transformations
- Extension of keypoints detection and descriptors construction to color images

## Medical image processing

*Andrey Nasonov, Alexander Semashko, Alexandra Nasonova, Vladmir Sergeev, Andrey Krylov*

Developing a system for automatical processing of retinal images to assist a doctor to make a diagnosis. The project includes:

- Detection of structural elements: optical disc, macula, blood vessels
- Detection of exudates
- Blood vessels analysis

*Nikolay Mamaev, Alexey Lukin, Dmitry Yurin*

The subject of this research is to develop effective algorithm for image filtering based on local pixels neighborhood decomposition by using Hermite functions.

## Audio signal analysis and processing

*Alexey Lukin, Maxim Tkachenko*

A spectral subtraction method for reduction of a stationary noise in audio signals leaves a well-known artifact called "musical noise" — a series of random energy bursts on a time-frequency plane. We are developing 2D smoothing methods for prevention of this artifact, and using multiresolution STFT techniques to improve time and frequency resolution of the method.

Filter banks with fixed time-frequency resolution, such as the Short-Time Fourier Transform (STFT), are a common tool for many audio analysis and processing applications allowing effective implementation via the Fast Fourier Transform (FFT). The fixed time-frequency resolution of the STFT can lead to the undesirable smearing of events in both time and frequency. We suggest adaptively varying STFT time-frequency resolution in order to reduce filter bank-specific artifacts while retaining adequate frequency resolution. Several strategies for systematic adaptation of time-frequency resolution are proposed. The introduced approach is demonstrated as applied to spectrogram displays, noise reduction, and spectral effects processing.

## Biometrics

*Elena Pavelyeva, Andrey Krylov*

Iris data pre-processing and parametrization by Hermite functions. Recognition of iris images.

Hermite projection method is used for human iris identification. Expansion of iris intensity information into a series of eigenfunctions of Fourier transform enables us to perform information analysis of the signal and its Fourier transform at the same time. Effectiveness of the method with test iris database images is shown.