Filip Sroubek

Multichannel blind iterative image restoration

Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a single-channel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvector-based method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

Multichannel blind deconvolution of spatially misaligned images

Existing multichannel blind restoration techniques assume perfect spatial alignment of channels, correct estimation of blur size, and are prone to noise. We developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary, and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process.

Identification of tuberculosis bacteria based on shape and color

Tuberculosis and other mycobacteriosis are serious illnesses which control is based on early diagnosis. A technique commonly used consists of analyzing sputum images for detecting bacilli. However, the analysis of sputum is time consuming and requires highly trained personnel to avoid high errors. Image-processing techniques provide a good tool for improving the manual screening of samples. In this paper, a new autofocus algorithm and a new bacilli detection technique is presented with the aim to attain a high specificity rate and reduce the time consumed to analyze such sputum samples. This technique is based on the combined use of some invariant shape features together with a simple thresholding operation on the chromatic channels. Some feature descriptors have been extracted from bacilli shape using an edited dataset of samples. A k-means clustering technique was applied for classification purposes and the sensitivity vs specificity results were evaluated using a standard ROC analysis procedure.

A Unified Approach to Superresolution and Multichannel Blind Deconvolution

This paper presents a new approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We do not assume any prior information about the shape of degradation blurs. The proposed approach consists of building a regularized energy function and minimizing it with respect to the original image and blurs, where regularization is carried out in both the image and blur domains. The image regularization based on variational principles maintains stable performance under severe noise corruption. The blur regularization guarantees consistency of the solution by exploiting differences among the acquired low-resolution images. Several experiments on synthetic and real data illustrate the robustness and utilization of the proposed technique in real applications.

Robust Multichannel Blind Deconvolution via Fast Alternating Minimization

Blind deconvolution, which comprises simultaneous blur and image estimations, is a strongly ill-posed problem. It is by now well known that if multiple images of the same scene are acquired, this multichannel (MC) blind deconvolution problem is better posed and allows blur estimation directly from the degraded images. We improve the MC idea by adding robustness to noise and stability in the case of large blurs or if the blur size is vastly overestimated. We formulate blind deconvolution as an l1 -regularized optimization problem and seek a solution by alternately optimizing with respect to the image and with respect to blurs. Each optimization step is converted to a constrained problem by variable splitting and then is addressed with an augmented Lagrangian method, which permits simple and fast implementation in the Fourier domain. The rapid convergence of the proposed method is illustrated on synthetically blurred data. Applicability is also demonstrated on the deconvolution of real photos taken by a digital camera.

Multifocus image fusion using the log-Gabor transform and a Multisize Windows technique

Today, multiresolution (MR) transforms are a widespread tool for image fusion. They decorrelate the image into several scaled and oriented sub-bands, which are usually averaged over a certain neighborhood (window) to obtain a measure of saliency. First, this paper aims to evaluate log-Gabor filters, which have been successfully applied to other image processing tasks, as an appealing candidate for MR image fusion as compared to other wavelet families. Consequently, this paper also sheds further light on appropriate values for MR settings such as the number of orientations, number of scales, overcompleteness and noise robustness. Additionally, we revise the novel Multisize Windows (MW) technique as a general approach for MR frameworks that exploits advantages of different window sizes. For all of these purposes, the proposed techniques are firstly assessed on simulated noisy experiments of multifocus fusion and then on a real microscopy scenario.

Self-Invertible 2D Log-Gabor Wavelets

Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. Alternative multiresolution transforms which specifically solve these drawbacks have been proposed. These transforms are generally overcomplete and consequently offer large degrees of freedom in their design. At the same time their optimization gets a challenging task. We propose here the construction of log-Gabor wavelet transforms which allow exact reconstruction and strengthen the excellent mathematical properties of the Gabor filters. Two major improvements on the previous Gabor wavelet schemes are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. Secondly, the set of filters cover uniformly the Fourier domain including the highest and lowest frequencies and thus exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is self-invertible). The present transform not only achieves important mathematical properties, it also follows as much as possible the knowledge on the receptive field properties of the simple cells of the Primary Visual Cortex (V1) and on the statistics of natural images. Compared to the state of the art, the log-Gabor wavelets show excellent ability to segregate the image information (e.g. the contrast edges) from spatially incoherent Gaussian noise by hard thresholding, and then to represent image features through a reduced set of large magnitude coefficients. Such characteristics make the transform a promising tool for processing natural images.

Blind Deconvolution Using Alternating Maximum a Posteriori Estimation with Heavy-Tailed Priors

Single image blind deconvolution aims to estimate the unknown blur from a single observed blurred image and recover the original sharp image. Such task is severely ill-posed and typical approaches involve some heuristic or other steps without clear mathematical explanation to arrive at an acceptable solution. We show that a straightforward maximum a posteriory estimation combined with very sparse priors and an efficient numerical method can produce results, which compete with much more complicated state-of-the-art methods.

Space-variant deblurring using one blurred and one underexposed image

We propose a practical method to remove photo blur due to camera shake, which is a typical problem when taking photos in dim lighting conditions such as indoor or night scenes. We use a pair of images, one of them blurred and the other one underexposed or noisy because of high ISO setting. Existing methods assume convolution model, that is the same blur in the whole image. It is seldom true in practice, especially for wide angle lens photos. We apply a space-variant model of blurring valid in many real situations. Results are documented by a photograph of a night scene.

Simultaneous super-resolution and blind deconvolution

In many real applications, blur in input low-resolution images is a nuisance, which prevents traditional super-resolution methods from working correctly. This paper presents a unifying approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We introduce a method which assumes no prior information about the shape of degradation blurs and which is properly defined for any rational (fractional) resolution factor. The method minimizes a regularized energy function with respect to the high-resolution image and blurs, where regularization is carried out in both the image and blur domains. The blur regularization is based on a generalized multichannel blind deconvolution constraint. Experiments on real data illustrate robustness and utilization of the method.