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We design an image quality measure independent of contrast changes, which are defined as a set of transformations preserving an order between the level lines of an image. This problem can be expressed as an isotonic regression problem. Depending on the definition of a level line, the partial order between adjacent regions can be defined through chains, polytrees or directed acyclic graphs. We provide a few analytic properties of the minimizers and design original optimization procedures together with a full complexity analysis. The methods worst case complexities range from O(n) for chains, to O (n log n) for polytrees and O (n 2 ϵ) for directed acyclic graphs, where n is the number of pixels and ϵ is a relative precision. The proposed algorithms have potential applications in change detection, stereo-vision, image registration, color image processing or image fusion. A C++ implementation with Matlab headers is available at https://github.com/pierre-weiss/contrast_invariant_snr. [ABSTRACT FROM AUTHOR]

We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on functions is a computationally intensive problem necessary for many practical problems. We analyze a technique called product-convolution expansion: The operator is locally approximated by a convolution, allowing to design fast numerical algorithms based on the fast Fourier transform. We design various types of expansions, provide their explicit rates of approximation and their complexity depending on the time-varying impulse response smoothness. This analysis suggests novel wavelet-based implementations of the method with numerous assets such as optimal approximation rates, low complexity and storage requirements as well as adaptivity to the kernels regularity. The proposed methods are an alternative to more standard procedures such as panel clustering, cross-approximations, wavelet expansions or hierarchical matrices. [ABSTRACT FROM AUTHOR]

We consider the problem of restoring images impaired by noise that is simultaneously structured and multiplicative. Our primary motivation for this setting is the selective plane illumination microscope which often suffers from severe inhomogeneities due to light absorption and scattering. This type of degradation arises in other imaging devices such as ultrasonic imaging. We model the multiplicative noise as a stationary process with known distribution. This leads to a novel convex image restoration model based on a maximum a posteriori estimator. After establishing some analytical properties of the minimizers, we finally propose a fast optimization method on GPU. Numerical experiments on 2D fluorescence microscopy images demonstrate the usefulness of the proposed models in practical applications. [ABSTRACT FROM AUTHOR]

Today, Light Sheet Fluorescence Microscopy (LSFM) makes it possible to image fluorescent samples through depths of several hundreds of microns. However, LSFM also suffers from scattering, absorption and optical aberrations. Spatial variations in the refractive index inside the samples cause major changes to the light path resulting in loss of signal and contrast in the deepest regions, thus impairing in-depth imaging capability. These effects are particularly marked when inhomogeneous, complex biological samples are under study. Recently, chemical treatments have been developed to render a sample transparent by homogenizing its refractive index (RI), consequently enabling a reduction of scattering phenomena and a simplification of optical aberration patterns. One drawback of these methods is that the resulting RI of cleared samples does not match the working RI medium generally used for LSFM lenses. This RI mismatch leads to the presence of low-order aberrations and therefore to a significant degradation of image quality. In this paper, we introduce an original optical-chemical combined method based on an adaptive SPIM and a water-based clearing protocol enabling compensation for aberrations arising from RI mismatches induced by optical clearing methods and acquisition of high-resolution in-depth images of optically cleared complex thick samples such as Multi-Cellular Tumour Spheroids. [ABSTRACT FROM AUTHOR]