Non-convex optimization for the design of sparse fir filters pdf

Wei, nonconvex optimization for the design of sparse fir filters, ieee workshop on statistical signal processing ssp, cardiff, uk, september 2009. We focus on the design of finite impulse response fir multiple notch filters. Optimization methods for nonlinearnonconvex learning problems. In addition to the literature on graphical models, our work is also closely related to a recent line of research on alternating minimization for. However, in contrast with conventional filterandsum beamformer, the passband steerability of fsbb is achieved at the cost of high complexity in structure, i. Existing theory yields useful performance criteria and processing techniques for acoustic pressuresensor arrays. In this regard, a number of evolutionary optimization based techniques have been applied for fir filter design. Why should nonconvexity be a problem in optimization. Nonconvex total variation regularization for convex denoising of signals.

Ist, wls, sparse filter, fir filter and digital filters i. They are composed of sparse sub lters whose high sparsity ensures fast image processing. Efficient design of sparse fir filters with optimized filter length. Most of the existing algorithms for sparse coding minimize a non convex function by heuristics like alternating minimization, gradient descent or their variants. This paper describes a new method for designing 1d and 2d sparse filters in the minimax sense using a mixture of reweighted l 1 minimization and greedy iterations. Optimization problem formulation for semidigital fir. View nonconvex optimization research papers on academia. Design of sparse fir filters with joint optimization of. Pdf recently, design of sparse finite impulse response fir digital filters has attracted. Wotao yin july 20 online discussions on those who complete this lecture will know the use of nonconvex regularization in sparse signal recovery geometry of pquasinorm 0 1 5 statistical proof frobenius norm max and spectral norm 6 experiments nonconvex statistical optimization for sparse tensor graphical modeldecember 1. First, an approximation function is introduced to reduce the nonconvex quadratically constrained optimization problem to a linearly constrained optimization problem. A necessary condition of optimality is derived for the subproblem of pnorm minimization, forming the basis for an efficient local.

Index termsfinite impulse response fir filter design, spectral mask. I was very surprised when i started to read something about non convex optimization in general and i saw statements like this. In the internet i came across global optimization algorithms like genetic algorithms, simulated annealing, etc but for solving a simple one variable unconstrained nonconvex optimization problem, i think using these high level algorithms doesnt seem to be a good idea. Efficient sparse group feature selection via nonconvex. The classical case is the singular value decomposition svd which is nonconvex but yet solvable. Modified artificial bee colony optimisation based fir. A set of analog metrics as hardware cost is also defined. Nov 28, 2018 optimization problem formulation for semidigital fir digitaltoanalog converter sdfir dac is investigated in this work. E cient sparse group feature selection via nonconvex optimization where a is an n by p data matrix with its columns representing di erent features. Many practical problems of importance are non convex, and most non convex problems are hard if not impossible to solve exactly in a reasonable time. Sparsity optimization in design of multidimensional filter networks mats andesson oleg burdakovy hans knutsson spartak zikriny abstract filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.

Performance analysis of socp and linear programming algorithms for sparse filter design. Consequently, we have devoted entire sections to present a tutoriallike treatment to basic concepts in convex analysis and optimization, as well as their non convex counterparts. Index termsfir filter design, coefficient sparsity, l0 approximation, peak error. Fir filter design via spectral factorization and convex. Non convex algorithms for group sparse optimization file. Wotao yin july 20 online discussions on those who complete this lecture will know the use of nonconvex regularization in sparse signal recovery geometry of pquasinorm 0 nov 12, 2014 sparse coding is a basic algorithmic primitive in many machine learning applications, such as image denoising, edge detection, compression and deep learning. Pdf acoustic vectorsensor array processing semantic. Request pdf design of sparse fir filters with joint optimization of sparsity and filter order in this paper, two novel algorithms are developed to design sparse linearphase lp fir filters. View non convex optimization research papers on academia.

Performance analysis of socp and linear programming. Nonconvex optimization and statistical inference xiang lyu will wei suny zhaoran wangz han liux jian yang guang chengk abstract we consider the estimation and inference of graphical models that characterize the dependency. Design of narrowband and wideband frequency response. Peakerrorconstrained sparse fir filter design using iterative. Local algorithms like gradient descent are widely used in nonconvex optimization, typically with few guarantees on performance. The lack of convexity for p finite impulse response fir multiple notch filters. A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. Sparsity optimization in design of multidimensional filter.

Non convex optimization for the design of sparse fir filters. Abstract this paper deals with a novel algorithm socp, which is used to design sparse fir filters. However, the nonlinear, non differentiable, non convex, multimodal nature of the associated optimization problem makes the design task quite challenging. Anthony april 22, 2004 2004c massachusetts institute of technology. Design and analysis framework for sparse fir channel shortening authors. Sparsityinducing nonconvex nonseparable regularization for convex image. However, the nonlinear, nondifferentiable, nonconvex, multimodal nature of the associated optimization problem makes the design task quite challenging. Despite their success in practice, they are not mathematically rigorous. A novel design of sparse prototype filter for nearly perfect. Publications by topic new york university tandon school of.

A major performance and complexity limitation in broadband communications is the long channel delay spread which results in a highlyfrequencyselective channel frequency response. Wotao yin july 20 online discussions on those who complete this lecture will know convex optimization background various standard concepts and terminology reformulating 1 optimization and its optimality conditions. Solving nonconvex optimization with global optimization. The lack of convexity for p optimization for the design of sparse fir. Nonconvex optimization through sequential convex programming pieter abbeel uc berkeley eecs. Design of narrowband and wideband frequencyresponse masking filters using sparse nonperiodic subfilters zaka ullah sheikh and oscar gustafsson department of electrical engineering, linko. Non convex optimization in machine learningnon convex optimization in machine learning generalized linear models have generally convex loss functions svms including non linear ones have convex loss functions, but have inequality constraints that make the problem difficult what samples are support vectors. The advantage of the l0model 1 lies in its complete control on two levels. Issues in nonconvex optimization mit opencourseware. In this paper, a novel algorithm is proposed to design sparse fir filters. Evolutionary algorithms have been found to be very effective for fir filter design because of the nonlinear, nondifferentiable.

A novel design of sparse fir multiple notch filters with. I was very surprised when i started to read something about nonconvex optimization in general and i saw statements like this. Pdf sparse fir filter design using binary particle swarm. Many practical problems of importance are nonconvex, and most non. Fir filter design by convex optimization using directed iterative.

This paper presents a method for designing sparse fir filters by means of a sequence of pnorm minimization problems with p gradually decreasing from 1 toward 0. Sparse signal estimation by maximally sparse convex optimization pdf arxiv. Nonconvex group sparsity signal decomposition via convex. Sparse fir filter design using binary particle swarm optimization. Constrained least square design of fir filters without specified transition bands. To reduce the computational complexity and hardware implementation complexity, a novel algorithm is developed based on the mixture of the tuning of notch frequencies and the sparsity of filter coefficients. In other cases, the nonconvex problem itself is shown to have no spurious local optima. Optimization problem formulation for semidigital fir digital. Relaxing the non convex problem to a convex problem convex neural networks strategy 3. Local nonconvex optimization convexity convergence rates apply escape saddle points using, for example, cubic regularization and saddlefree newton update strategy 2. It is known that this design problem is highly nonconvex due to the existence of. Dec 21, 2017 a vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. Fir filter design via spectral factorization and convex optimization. Pdf sparse fir filter design based on simulated annealing.

In addition to the literature on graphical models, our work is also closely related to a recent line of research on alternating minimization for nonconvex optimization problems 10. The associated optimization problems, with the filter coefficients as the variables and the frequency response bounds as constraints, are in general nonconvex. In other cases, the non convex problem itself is shown to have no spurious local optima. The farrowstructurebased steerable broadband beamformer fsbb is particularly useful in the applications where sound source of interest may move around a wide angular range. Optimization problem formulation for semidigital fir digitaltoanalog converter sdfir dac is investigated in this work.

The lack of convexity for p sparse fir filters by means of a sequence of pnorm minimization problems with p gradually decreasing from 1 toward 0. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a nonconvex function. Consequently, we have devoted entire sections to present a tutoriallike treatment to basic concepts in convex analysis and optimization, as well as their nonconvex counterparts. Ivan selesnick electrical and computer engineering. We consider the design of finite impulse response fir filters subject to upper and lower bounds on the frequency response magnitude. However, design of sparse fir filter under the prescribed constraints is a highly nonconvex l 0 norm problem, which cannot be effectively solved in polynomial time 19. The classical case is the singular value decomposition svd which is non convex but yet solvable. Peakerrorconstrained sparse fir filter design using. In the internet i came across global optimization algorithms like genetic algorithms, simulated annealing, etc but for solving a simple one variable unconstrained non convex optimization problem, i think using these high level algorithms doesnt seem to be a good idea. However, design of sparse fir filter under the prescribed constraints is a highly non convex l 0 norm problem, which cannot be effectively solved in polynomial time 19. The lack of convexity for p pdf iterative reweighted l 1 design of sparse fir filters sparse fir filters have lower implementation complexity than full filters, while keeping a good performance level. Iterative reweighted l1 design of sparse fir filters. The proposed design procedure can be carried out as follow.

Nonconvex optimization in machine learningnonconvex optimization in machine learning generalized linear models have generally convex loss functions svms including nonlinear ones have convex loss functions, but have inequality constraints that make the problem difficult what samples are support vectors. Non convex statistical optimization for sparse tensor graphical model december 1, 2016 non convex statistical optimization for sparse tensor graphical modeldecember 1, 2016 1 30. Nonconvex statistical optimization for sparse tensor. In this note, we address the theoretical properties of. Fir filter optimization with pos3poly in cvx eurasip. Chebyshev optimization of sparse fir filters using linear programming with an application to.

Optimisation based design of finite impulse response fir filters has been an active area of research for quite some time. Optimization under nonconvex quadratic matrix inequality. Modified artificial bee colony optimisation based fir filter. Oppenheim, sampling based on local bandwidth, asilomar conference on signals, systems, and computers, pacific grove, ca, november 2007. Nonconvex group sparsity signal decomposition via convex optimization for bearing fault diagnosis. Sparse fir filters have lower implementation complexity than full filters, while keeping a good performance level. Aug 11, 2009 non convex optimization algorithms for group sparsity solves a dummy ofdm sparse channel estimation problem. Publications by topic new york university tandon school. Optimization under nonconvex quadratic matrix inequality constraints with application to design of optimal sparse controller.

Convex denoising using nonconvex tight frame regularization. Pdf design of sparse finite impulse response fir filter is of great. Local non convex optimization convexity convergence rates apply escape saddle points using, for example, cubic regularization and saddlefree newton update strategy 2. Pdf nonconvex optimization for the design of sparse fir. In this paper, we introduce a new design framework based on the recently proposed semide.

Wei, nonconvex optimization for the design of sparse fir filters. Sparse fir filter design, where some tap weights are zero, is of interest as a means of reducing the expense or enhancing the performance of a filter, as a result of fewer or more efficiently. The various algorithms proposed for fir filter design aim at meeting a set of desired specifications in the frequency domain. Chebyshev design of fir filters with arbitrary magnitude and phase responses.

In this paper, the nonconvex design problem is modeled as a combinatorial optimization. This thesis develops new analysis and processing techniques for. Non convex optimization algorithms for group sparsity solves a dummy ofdm sparse channel estimation problem. Citeseerx document details isaac councill, lee giles, pradeep teregowda.

Abstract this paper deals with a novel algorithm socp, which is. There has been recently a flurry of new results on provable nonconvex methods which can be guaranteed to converge to the global optimum. This is especially true of algorithms that operate in high. Nonconvex optimization for the design of sparse fir filters. Fir filter design is one of the main beneficiaries of the devel opments in convex. First, an approximation function is introduced to reduce the non convex quadratically constrained optimization problem to a linearly constrained optimization problem. A novel algorithm is presented in this paper to design sparse fir filters in the weighted. Review and analysis of evolutionary optimizationbased. Acoustic vectorsensor arrays, which measure particle velocity and pressure, offer significant potential but require fundamental changes to algorithms and performance assessment. Then, the desired sparse linear phase fir prototype filter is derived through the orthogonal matching pursuit omp performed under the weighted l 2 norm.

Efficient design of sparse fir filters with optimized. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non convex function. Citeseerx sparse recovery by nonconvex optimization. Optimization methods for nonlinearnonconvex learning.