Benefits of consistency in image denoising with steerable wavelets

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms applicable to images with a high amount of directional features. However, arbitrary modification of the wavelet-domain coefficients may violate consistency constraints because a legitimate representation must be redundant. In this paper, by honoring the redundancy of the coefficients, we demonstrate that it is possible to improve the performance of regularized least-squares problems in the steerable wavelet domain. We illustrate that our consistent method significantly improves upon the performance of conventional denoising with steerable wavelets

Phosphorylation does not prompt, nor prevent, the formation of α-synuclein toxic species in a rat model of Parkinson's disease

Phosphorylation is involved in numerous neurodegenerative diseases. In particular, alpha-synuclein is extensively phosphorylated in aggregates in patients suffering from synucleinopathies. However, the share of this modification in the events that lead to the conversion of alpha-synuclein to aggregated toxic species needed to be clarified. The rat model that we developed through rAAV2/6-mediated expression of alpha-synuclein demonstrates a correlation between neurodegeneration and formation of small filamentous alpha-synuclein aggregates. A mutation preventing phosphorylation (S129A) significantly increases alpha-synuclein toxicity and leads to enhanced formation of beta-sheet-rich, proteinase K-resistant aggregates, increased affinity for intracellular membranes, a disarrayed network of neurofilaments and enhanced alpha-synuclein nuclear localization. The expression of a mutation mimicking phosphorylation (S129D) does not lead to dopaminergic cell loss. Nevertheless, fewer but larger aggregates are formed, and signals of apoptosis are also activated in rats expressing the phosphorylation-mimicking form of alpha-synuclein. These observations strongly suggest that phosphorylation does not play an active role in the accumulation of cytotoxic pre-inclusion aggregates. Unexpectedly, the study also demonstrates that constitutive expression of phosphorylation-mimicking forms of alpha-synuclein does not protect from neurodegeneration. The role of phosphorylation at Serine 129 in the early phase of Parkinson's disease is examined, which brings new perspective to therapeutic approaches focusing on the modulation of kinases/phosphatases activity to control alpha-synuclein toxicit

Rotational Features Extraction for Ridge Detection

State-of-the-art approaches to detecting ridge-like structures in images rely on filters designed to respond to locally linear intensity features. While these approaches may be optimal for ridges whose appearance is close to being ideal, their performance degrades quickly in the presence of structured noise that corrupts the image signal, potentially to the point where it truly does not conform to the ideal model anymore. In this paper, we address this issue by introducing a learning framework that relies on rich, local, rotationally invariant image descriptors and demonstrate that we can outperform state-of-the-art ridge detectors in many different kinds of imagery. More specifically, our framework yields superior performance for the detection of blood vessel in retinal scans, dendrites in bright-field and confocal microscopy image-stacks, and streets in satellite imagery

Closed-Form Expression of the Fourier Ring-Correlation for Single-Molecule Localization Microscopy

Single-molecule localization microscopy (SMLM) is a popular microscopic technique that achieves super resolution imaging by localizing individual blinking molecules in thousands of frames. Therefore, the reconstructed high-resolution image is a combination of millions of point sources. This particular computational reconstruction leads to the question of the estimation of the image resolution. Fourier-ring correlation (FRC) is the standard tool for assessing the resolution. It has been proposed for SMLM by computing a discrete correlation in the Fourier domain. In this work, we derive a closed-form expression to compute the continuous FRC. Our implementation provides an exact FRC and an alternative to compute a parameter-free FRC. In addition, it gives insights on the discrepancy of the discrete FRC and yields a rule to select its parameters such as the spatial sampling step or the width of the kernel used as density estimator

Deforming Tessellations for the Segmentation of Cell Aggregates

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is encoded by control points grouped in tiles. The smooth and continuously defined boundary of each tile is generated by recursively applying a refinement process to its control points. We deform the smooth tessellation in a global manner using a ridge-based energy that we have designed for that purpose. By construction, cells are segmented without overlap and the tessellation structure is maintained even on dim membranes. Leakage, which afflicts usual image-processing methods (e.g., watershed), is thus prevented. We validate our framework on both synthetic and real microscopy images, showing that the proposed method is robust to membrane gaps and to high levels of noise

Transforms and Operators for Directional Bioimage Analysis: A Survey

We give a methodology-oriented perspective on directional image analysis and rotation-invariant processing. We review the state of the art in the field and make connections with recent mathematical developments in functional analysis and wavelet theory. We unify our perspective within a common framework using operators. The intent is to provide image-processing methods that can be deployed in algorithms that analyze biomedical images with improved rotation invariance and high directional sensitivity. We start our survey with classical methods such as directional-gradient and the structure tensor. Then, we discuss how these methods can be improved with respect to robustness, invariance to geometric transformations (with a particular interest in scaling), and computation cost. To address robustness against noise, we move forward to higher degrees of directional selectivity and discuss Hessian-based detection schemes. To present multiscale approaches, we explain the differences between Fourier filters, directional wavelets, curvelets, and shearlets. To reduce the computational cost, we address the problem of matching directional patterns by proposing steerable filters, where one might perform arbitrary rotations and optimizations without discretizing the orientation. We define the property of steerability and give an introduction to the design of steerable filters. We cover the spectrum from simple steerable filters through pyramid schemes up to steerable wavelets. We also present illustrations on the design of steerable wavelets and their application to pattern recognition

Exact Complex-Wave Reconstruction in Digital Holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique. (C) 2011 Optical Society of Americ

Artifact-free reconstruction from off-axis digital holograms through nonlinear filtering

We present experimental investigation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object auto-correlation, commonly called the zero-order term, from holographic measurements, thereby suppressing the artifacts generated by the intensities of the two beams employed for interference from complex wavefield reconstruction. The algorithm is based on non-linear filtering, and can be applied to standard DHM setups, with realistic recording conditions. We study the applicability of the technique under different experimental configurations, such as topographic images of microscopic specimens or speckle holograms

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our method consists in restricting the search space to splines with knots on a uniform grid, which results in a standard convex finite-dimensional problem. As basis functions for this search space, we use the B-splines matched to the regularization order, which are optimally localized. This leads to a well-conditioned, computationally feasible optimization task. Our proposed iterative multiresolution algorithm then refines the grid size until a desired level of accuracy is met and converges to sparse solutions of our inverse problem. Finally, we present experimental results that validate our approach