Maximum likelihood estimation of a class of non-Gaussian densities with application to deconvolution

Pham, Trung Tat; deFigueiredo, R.J.P.

doi:10.1109/icassp.1987.1169626

Cited by 19 publications

(18 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above quadratic form of Ψ corresponds to white Gaussian noise {n i }. Recall that many papers are dedicated to the minimization of Ψ(., y) alone and of the form (3), i.e., F = Ψ, mainly for ψ(t) = t 2 [22], in some cases for ψ(t) = |t| [8], but functions ψ(t) = |t| ρ for different values for ρ in the range (0, ∞] also have been considered [31,30]. Specific data-fidelity terms arise in applications such as emission and transmission computed tomography, X-ray radiography, eddy-currents evaluation, and many others [23,20,34,10].…”

Section: Introductionmentioning

confidence: 99%

Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

Nikolova¹

2002

SIAM J. Numer. Anal.

305

232

View full text Add to dashboard Cite

Abstract. We present a theoretical study of the recovery of an unknown vector x ∈ R p (such as a signal or an image) from noisy data y ∈ R q by minimizing with respect to x a regularized costfunction F (x, y) = Ψ(x, y) + αΦ(x), where Ψ is a data-fidelity term, Φ is a smooth regularization term, and α > 0 is a parameter. Typically, Ψ(x, y) = Ax − y 2 , where A is a linear operator. The data-fidelity terms Ψ involved in regularized cost-functions are generally smooth functions; only a few papers make an exception to this and they consider restricted situations. Nonsmooth data-fidelity terms are avoided in image processing. In spite of this, we consider both smooth and nonsmooth data-fidelity terms. Our goal is to capture essential features exhibited by the local minimizers of regularized cost-functions in relation to the smoothness of the data-fidelity term.In order to fix the context of our study, we consider Ψ(x, y) = i ψ(a T i x − y i ), where a T i are the rows of A and ψ is C m on R \ {0}. We show that if ψ (0 − ) < ψ (0 + ), then typical data y give rise to local minimizersx of F (., y) which fit exactly a certain number of the data entries: there is a possibly large setĥ of indexes such that a T ix = y i for every i ∈ĥ. In contrast, if ψ is smooth on R, for almost every y, the local minimizers of F (., y) do not fit any entry of y. Thus, the possibility that a local minimizer fits some data entries is due to the nonsmoothness of the data-fidelity term. This is a strong mathematical property which is useful in practice. By way of application, we construct a cost-function allowing aberrant data (outliers) to be detected and to be selectively smoothed. Our numerical experiments advocate the use of nonsmooth data-fidelity terms in regularized cost-functions for special purposes in image and signal processing.

show abstract

Section: Introductionmentioning

confidence: 99%

Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

Nikolova¹

2002

SIAM J. Numer. Anal.

305

232

View full text Add to dashboard Cite

show abstract

“…Equation (16) can be rewritten by classifying the coding types as (17), shown at the bottom of the page, where and are the numbers of intra-and nonintra-coded blocks, is the DCT coefficient of the component of the th block, is the DCT coefficient of the component of the th intra-block, is the DCT coefficient of the component of the th predicting block.…”

Section: A the Energy Of Video Sequencementioning

confidence: 99%

Nonreference Method for Estimating PSNR of MPEG-2 Coded Video by Using DCT Coefficients and Picture Energy

Ichigaya¹,

Nakasu²

2008

IEEE Trans. Circuits Syst. Video Technol.

View full text Add to dashboard Cite

Irreversible video coding like MPEG-2 may cause deterioration in picture quality depending on the properties of the source images and coding type. A monitoring technology to assess picture quality with fluctuations is needed for digital video services. We previously proposed a method to estimate the peak signal-tonoise-ratio (PSNR) of MPEG-2 coded video by using bit stream information. The method is categorized as a nonreference measurement that does not use source signals. It estimates the amount of distortion in each frame by analyzing the information in the decoded DCT coefficients. This paper describes a way to improve the accuracy of the PSNR estimation of our previous method, especially for the not coded blocks. The proposed method utilizes the temporal fluctuations of ac energy and estimates the PSNR of not-coded blocks from the inter-frame correlation of the decoded pictures. Experimental results show that the determination coefficient 2 between estimated and actual PSNRs is above 0.95 for every type of picture frame.Index Terms-AC energy, discrete cosine transform (DCT) information, MPEG-2, nonreference method, not-coded blocks, peak signal-to-noise ratio (PSNR).

show abstract

“…In recent years, many algorithms have been developed that learn a transform basis adapted to the statistics of the input signals. Two widely used learning algorithms are principal component analysis (PCA), which finds an orthogonal basis using second-order statistics [2], and independent component analysis (ICA) which finds a non-orthogonal representation using higher order statistics [3,4]. The set of bases used by PCA and ICA are complete or undercomplete, i.e., the matrix defining the transformation A 2 R mÂn has m !…”

Section: Introductionmentioning

confidence: 99%

Learning Sparse Overcomplete Codes for Images

Murray

Kreutz-Delgado

2006

J VLSI Sign Process Syst Sign Image Video Technol

View full text Add to dashboard Cite

Abstract. Images can be coded accurately using a sparse set of vectors from a learned overcomplete dictionary, with potential applications in image compression and feature selection for pattern recognition. We present a survey of algorithms that perform dictionary learning and sparse coding and make three contributions. First, we compare our overcomplete dictionary learning algorithm (FOCUSS-CNDL) with overcomplete independent component analysis (ICA). Second, noting that once a dictionary has been learned in a given domain the problem becomes one of choosing the vectors to form an accurate, sparse representation, we compare a recently developed algorithm (sparse Bayesian learning with adjustable variance Gaussians, SBL-AVG) to well known methods of subset selection: matching pursuit and FOCUSS. Third, noting that in some cases it may be necessary to find a non-negative sparse coding, we present a modified version of the FOCUSS algorithm that can find such non-negative codings. Efficient parallel implementations in VLSI could make these algorithms more practical for many applications.

show abstract

Maximum likelihood estimation of a class of non-Gaussian densities with application to deconvolution

Cited by 19 publications

References 5 publications

Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

Nonreference Method for Estimating PSNR of MPEG-2 Coded Video by Using DCT Coefficients and Picture Energy

Learning Sparse Overcomplete Codes for Images

Contact Info

Product

Resources

About