Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1) building the optimal linear subspace approximation with orthonormal bases using the second-order statistics of input vectors, 2) augmenting each transform kerne...

The integral of a function defined on the half-plane along the semi-circles centered on the boundary of the half-plane is known as the circular averages transform. Circular averages transform arises in many tomographic image reconstruction problems. In particular, in synthetic aperture radar (SAR) when the transmitting and receiving antennas are colocated, the received signal is modeled as the ...

we prove a novel result using the higher-order stationary phase approximation: we show convergence of the normalized power spectrum (squared magnitude of the Fourier transform) of the wave function to the density function of the distance transform gradients as the free parameter τ → 0. In colloquial terms, spatial frequencies are gradient histogram bins. Since distance transform gradients carry...

Abstract This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed by the ridgelet transform with respect to Lizorkin distributions. By showing three reconstruction formulas by using the Fourier slice the...

Image Fusion is a combination of two or more different images. It extracts the information from multiple source images. Wavelet based image fusion is suitable for representing the point singularities in one dimensions, but it fails to represent the edges across the curves in two dimensions. In this method, pixel level fusion based on curvelet transform detects the discontinuities across the cur...

In this paper, a new fragile watermarking method for digital image authentication is proposed based on the zero locations of the -transform. The -transform domain is a new transform space for fragile watermark embedding. Our watermarking method is designed by exploiting the sensitivity of the positions of the zeroes of the -transform around the unit circle to any change made on the host image. ...

Complementing recent advances made in the field of structural health monitoring and damage detection, the concept of a wireless sensing network with distributed computational power is proposed. The fundamental building block of the proposed sensing network is a wireless sensing unit capable of acquiring measurement data, interrogating the data and transmitting the data in real time. The computa...

We evaluate performances of different implementations of affine transform in motion compensation architecture based on a hierarchical adaptive structured mesh. The architecture predicts the next video frame using the reference frame, mesh code and mesh node motion vectors. It achieves significant reduction in describing the mesh topology by coding the splitting in recursive triangulation of the...