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Sparse coding techniques for image processing traditionally rely on processing small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the $\ell_0$ ``norm'' of the whole image, which may create an imbalanced sparsity across various regions in the image.


The problem of identification of a nonstationary autoregressive process
with unknown, and possibly time-varying, rate of parameter
changes, is considered and solved using the parallel estimation approach.
The proposed two-stage estimation scheme, which combines
the local estimation approach with the basis function one, offers
both quantitative and qualitative improvements compared with
the currently used single-stage methods.


Approximating the transfer function of stable causal linear systems by a basis expansion is a common task in signal- and system theory. This paper characterizes a scale of signal spaces, containing stable causal transfer functions, with a very simple basis (the Fourier basis) but which is not computable. Thus it is not possible to determine the coefficients of this basis expansion on any digital computer such that the approximation converges to the desired function.


We develop two techniques based on alternating minimization and
alternating directions method of multipliers for phase retrieval (PR)
by employing a variable-splitting approach in a maximum likelihood
estimation framework. This leads to an additional equality constraint,
which is incorporated in the optimization framework using a
quadratic penalty. Both algorithms are iterative, wherein the updates
are computed in closed-form. Experimental results show that: (i)
the proposed techniques converge faster than the state-of-the-art PR


Uncertainty principles in finite dimensional vector space have been studied extensively, however they cannot be applied to sparse representation of rational functions. This paper considers the sparse representation for a rational function under a pair of orthonormal rational function bases. We prove the uncertainty principle concerning pairs of compressible representation of rational functions in the infinite dimensional function space. The uniqueness of compressible representation using such pairs is provided as a direct consequence of uncertainty principle.


In this paper, we propose single depth image super-resolution using convolutional neural networks (CNN). We adopt CNN to acquire a high-quality edge map from the input low-resolution (LR) depth image. We use the high-quality edge map as the weight of the regularization term in a total variation (TV) model for super-resolution. First, we interpolate the LR depth image using bicubic interpolation and extract its low-quality edge map. Then, we get the high-quality edge map from the low-quality one using CNN.


Estimating envelope of a signal has various applications including empirical mode decomposition (EMD) in which the cubic $C^2$-spline based envelope estimation is generally used. While such functional approach can easily control smoothness of an estimated envelope, the so-called undershoot problem often occurs that violates the basic requirement of envelope. In this paper, a tangentially constrained spline with tangential points optimization is proposed for avoiding the undershoot problem while maintaining smoothness.