Incoherent Frames Research Articles

Incoherent frames design and dictionary learning using a distance barrier

We present a unitary approach to the design of incoherent frames and to dictionary learning, by using a single function that promotes incoherence for both problems. This function has a context-dependent quadratic term and a distance barrier term that was never used in this context. We provide simple and efficient algorithms for both problems. Numerical results show that we can obtain large frames whose incoherence is better than of those designed by other methods. Also, in dictionary learning, we can improve both the representation error and the incoherence of the dictionary, compared with the standard approach.

Algorithms for the construction of incoherent frames under various design constraints

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low coherence frames are useful in compressed sensing applications. When used as measurement matrices, they successfully recover highly sparse solutions to linear inverse problems. This paper describes algorithms for the design of various low coherence frame types: real, complex, unital (constant magnitude) complex, sparse real and complex, nonnegative real and complex, and harmonic (selection of rows from Fourier matrices). The proposed methods are based on solving a sequence of convex optimization problems that update each vector of the frame. This update reduces the coherence with the other frame vectors, while other constraints on its entries are also imposed. Numerical experiments show the effectiveness of the methods compared to the Welch bound, as well as other competing algorithms, in compressed sensing applications.

Passive Radar Array With Low-Power Satellite Illuminators Based on Fractional Fourier Transform

This paper addresses the detection of surface slow moving targets by means of an array passive radar based on low-EIRP satellite illuminators of opportunity. Particularly, the use of the receiving array of K elements is considered to provide increased detection capability for targets with limited radar cross section, together with the capability to estimate the target direction-of-arrival. A full processing scheme is proposed to exploit together both the long integration times and the multiple receiving elements. This includes a coherent space-time integration of the signal received at the K antenna elements during short frames, followed by an incoherent frame to frame integration. The proposed scheme is based on the fractional Fourier transform that is shown to map the signals into a natural rotated frequency-angle plane, where we can easily compensate the target Doppler frequency shifts available at the different antenna elements and temporal frames. Its effectiveness is shown by application to different synthetic scenarios, where the target detection is only achievable when all the possible integration gain is capitalized.

Incoherent Unit-Norm Frame Design via an Alternating Minimization Penalty Method

This letter is concerned with designing incoherent unit-norm frames, i.e., a set of vectors in a finite dimensional Hilbert space with unit norms and very low absolute pairwise correlations. Due to their widespread use in a variety of applications, including compressed sensing and coding theory, incoherent frame design has received considerable attention, and many algorithms have been proposed to this aim. In this letter, a new algorithm is presented which constructs incoherent frames by minimizing the maximum absolute pairwise correlations (mutual coherence) of the frame vectors. Our strategy is based on an alternating minimization penalty method, which admits efficient solvers using proximal algorithms. Experimental results on designing incoherent frames of various dimensions show that our algorithm outperforms some recent methods in the literature.

Designing Incoherent Frames Through Convex Techniques for Optimized Compressed Sensing

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have focused on minimizing the absolute value off-diagonal entries of the Gram matrix of these structures. Recently, a method based on convex optimization that operates directly on the vectors of the frame has been shown to produce promising results. This paper gives a detailed analysis of the optimization problem at the heart of this approach and, based on these insights, proposes a new method that substantially outperforms the initial approach and all current methods in the literature for all types of frames, with low and high redundancy. We give extensive experimental results that show the effectiveness of the proposed method and its application to optimized compressed sensing.

Civil society and global copyright reform advocacy: incoherent frames as missed opportunities?

After almost a decade of civil society (CS) efforts aimed at reforming the global intellectual property (IP) system, this study examines whether the paucity in global copyright reform is a result of the failure by civil society to mobilise around an explicit or coherent frame. While previous episodes of global intellectual property rights (IPR) reform advocacy involving CS were effectively contested under a human rights frame, there have been less successful framing attempts in the space of copyright reform advocacy. Using semi-structured interviews with key civil society stakeholders involved in the reform of the global copyright system, the study explores possible explanations for this lapse in framing in copyright reform advocacy. It also questions the extent to which framing has been an intelligible lens through which to understand the success or failure of global IPR advocacy. It reveals that frame analysis does not comprehensively capture success or failure in global IPR policymaking. Lastly, the study looks at problems with civil society and what these mean for copyright reform and ultimately the future of the global IPR system.

Ultrasonic imaging contrast enhancement using modified dehaze image model

In practical ultrasonic images, post-processing that involves incoherent frame averaging such as persistence, spatial compounding and frequency compounding creates a layer of smoothed out electronic noise that is analogous to fog in photographic images. A novel approach to enhance ultrasound image contrast based on a modified dark channel model used to dehaze photographs is presented. Local minimum intensity is used to highlight image contrast, control influence of noise layer and improve detail resolution by different levels. The experimental results show that the proposed method has better performance over the existing methods in improving the quality of the ultrasonic image.

Design of Incoherent Frames via Convex Optimization

This paper describes a new procedure for the design of incoherent frames used in the field of sparse representations. We present an efficient algorithm for the design of incoherent frames that works well even when applied to the construction of relatively large frames. The main advantage of the proposed method is that it uses a convex optimization formulation that operates directly on the frame, and not on its Gram matrix. Solving a sequence of convex optimization problems allows for the introduction of constraints on the frame that were previously considered impossible or very hard to include, such as non-negativity. Numerous experimental results validate the approach.

Depersonalisation/derealisation symptoms in vestibular disease

Background: Depersonalisation is a subjective experience of unreality and detachment from the self often accompanied by derealisation; the experience of the external world appearing to be strange or unreal. Feelings...