Smokey Robinson - The Tracks Of My Tear

In ''American Idol" Season 08, Episode 23 (March 25, 2009), Adam Lambert gave us an awesome performance.

Lyrics:

People say I'm the life of the party
'Cause I tell a joke or two
Although I might be laughin' loud and hearty
Deep inside I'm blue

So take a good look at my face
You'll see my smile looks out of place
If you look closer it's easy to trace
The tracks of my tears

I need you (need you)
Need you (need you)

Since you left me if you see me with another girl
Seemin' like I'm havin' fun
Although she may be cute
She's just a substitute
Because you're the permanent one

So take a good look at my face, uh-huh
You see my smile (looks out of place)
Yeah, look a little bit closer
It's easy to trace, oh the tracks of my tears

Oh-ho-ho-ho I need you (need you)
Need you (need you)

Hey hey -yeah
(Outside) i'm masquerading
(Inside) all my hope is fading
(Im just a clown) ooo-yeah, since you put me down
My smile is my make-up
I wear since my break-up with you

Baby, take a good look at my face, uh-huh
You see my smile looks (out of place)
Yeah, just look closer it's easy (to trace)
Oh, the tracks of my tears

Baby, baby, baby, baby
Take a good look at (my face)
Ooo, yeah you see my smile (looks out of place)
Look a little bit closer (it's easy to trace)
Yeah, the tracks of my tears, oh yeah
FADES-
Baby, take a good look

Cylindrical lens & Reflection Tomography

Cylindrical lens

A cylindrical lens is a lens which focuses light which passes through onto a line instead of onto a point, as a spherical lens would. The curved face or faces of a cylindrical lens are sections of a cylinder, and focus the image passing through it onto a line parallel to the intersection of the surface of the lens and a plane tangent to it. The lens compresses the image in the direction perpendicular to this line, and leaves it unaltered in the direction parallel to it (in the tangent plane). (From Wikipedia, the free encyclopedia)

Reflection Tomography

The basic aim of reflection tomography is to construct a quantitative cross-sectional image from reflection data. One nice aspect of this form of imaging, especially in comparison with transmission tomography (i.e. Diffraction Tomography), is that it is not necessary to encircle the object with transmitters and receivers for gathering the “projection” data; transmission and reception are now done from the same side.

Transmission tomography is sometimes not possible because of physical constraints. For example, when ultrasound is used for cardiovascular imaging, the transmitted signal is almost immeasurable because of large impedance discontinuities at tissue-bone and air-tissue interfaces and other attenuation losses. For this reason most medical ultrasonic imaging is done using reflected signals.

As for the mathematical model of reflection tomography, the measured time-domain reflected waveform for viewing angle theta can be written as:
where pt is the incident pulse, c is the speed of light within the slice, is the projection of the object slice which are related to the object reflectivity edge map/function f. According to "Principles of Computerized Tombgraphic Imaging" by Avinash C. Kak and Malcolm Slaney, each measured waveform can be considered as a convolution of the parellel projection of the object's 2-D reflectivity function with the incident pulse, just as the first equation above. Thereby, the line projection can be recovered with a deconvolution method, e.g:
where represent the Fourier transform of the corresponding time or space domain signal. However, I actually have no idea about how can I get this equation. I tried to get it from the definition of the Fourier transform, but failed. Hornestly, I don't understand why this equation can be thought as a convolution. Just because of its format?

In practice, of course, one may have to resort to techniques such as Wiener filtering for implementing the frequency domain inversion. In "Terahertz wide aperture reflection tomography", they usd a hybrid Fourier-wavelet regularized deconvolution algorithm to retrieve from , "because it minimizes the artifacts that are associated with pure Fourier-basedapproaches".

Some SPARS'09 papers about CS (2)

Here are some other papers that will presented at SPARS'09:

Contextual Image Compression from Adaptive Sparse Data Representations by Laurent Demaret, Armin Iske, Wahid Khachabi. The abstract reads:

Natural images contain crucial information in sharp geometrical boundaries between objects. Therefore, their description by smooth isotropic function spaces (e.g. Sobolev or Besov spaces) is not sufficiently accurate. Moreover, methods known to be optimal for such isotropic spaces (tensor product wavelet decompositions) do not provide optimal nonlinear approximations for piecewise smooth bivariate functions. Among the geometry based alternatives that were proposed during the last few years, adaptive thinning methods work with continuous piecewise affine functions on anisotropic triangulations to construct sparse representations for piecewise smooth bivariate functions. In this article, a customized compression method for coding the sparse data information, as output by adaptive thinning, is proposed. The compression method is based on contextual encoding of both the sparse data positions and their attached luminance values. To this end, the structural properties of the sparse data representation are essentially exploited. The resulting contextual image compression method of this article outperforms our previous methods (all relying on adaptive thinning) quite significantly. Moreover, our proposed compression method also outperforms JPEG2000 for selected natural images, at both low and middle bitrates, as this is supported by numerical examples in this article.

Compressive Domain Interference Cancellation by Mark A. Davenport, Petros T. Boufounos, Richard Baraniuk. The abstract reads:

In this paper we consider the scenario where a compressive sensing system acquires a signal of interest corrupted by an interfering signal. Under mild sparsity and orthogonality conditions on the signal and interference, we demonstrate that it is possible to efficiently filter out the interference from the compressive measurements in a manner that preserves our ability to recover the signal of interest. Specifically, we develop a filtering method that nulls out the interference while maintaining the restricted isometry property (RIP) on the set of potential signals of interest. The construction operates completely in the compressive domain and has computational complexity that is polynomial in the number of measurements.

Algorithms for Multiple Basis Pursuit Denoising by Alain Rakotomamonjy. The abstract reads:

We address the problem of learning a joint sparse approximation of several signals over a dictionary. We pose the problem as a matrix approximation problem with a row-sparsity inducing penalization on the coefficient matrix. We propose a simple algorithm based on iterative shrinking for solving the problem. At the present time, such a problem is solved either by using a Second-Order Cone programming or by means of a MFocuss algorithm. While the former algorithm is computationally expensive, the latter is efficient but present some pitfalls like presences of fixed points which are undesiderable when solving a convex problem. By analyzing the optimality conditions of the problem, we derive a simple algorithm. The algorithm we propose is efficient and is guaranteed to converge to the optimal solution, up to a given tolerance. Furthermore, by means of a reweighted scheme, we are able to improve the sparsity of the solution.

*The Two Stage l1 Approach to the Compressed Sensing Problem by Stéphane Chrétien. The abstract reads:

This paper gives new results on the recovery of sparse signals using l1-norm minimization. We introduce a two stage l1 algorithm equivalent to the first two iterations of the alternating l1 relaxation introduced in [1].

*General Perturbations in Compressed Sensing by Matthew A. Herman, Thomas Strohmer. The abstract reads:

We analyze the Basis Pursuit recovery of signals when observing K-sparse data with general perturbations (i.e., additive, as well as multiplicative noise). This completely perturbed model extends the previous work of Candes, Romberg and Tao on stable signal recovery from incomplete and inaccurate measurements. Our results show that, under suitable conditions, the stability of the recovered signal is limited by the noise level in the observation. Moreover, this accuracy is within a constant multiple of the best-case reconstruction using the technique of least squares.

Reconstruction of Undersampled Cardiac Cine MRI data Using Compressive Sensing Principles by Pooria Zamani, Hamid Soltanian-Zadeh. The abstract reads:

Reduction of MRI data acquisition time is an important goal in the MRI field. Undersampling k-t space is a solution to reduce acquisition time. MR images may have sparse or compressible presentations in appropriate transform domains, such as wavelets. According to the Compressive Sensing (CS) theory, they can be recovered from randomly undersampled k-t space data that guarantees incoherency between sparsifying transform and sampling operator. However, pure random k-space sampling can be more time-consuming than full k-space sampling because of MRI principles. In this paper, we propose a new method based on hidden Markov models (HMM) to undersample k-space along the phase-encoding direction. To this end, we cluster extracted features of each k-space line by fuzzy c-means (FCM) method and consider the resulting class labels as the states of a Markov chain. Then we train a HMM and find the related transition matrix to each k-space line. We choose the lines having more non-diagonal transition matrices to sample data along them. We reconstruct the image by minimizing the L1 norm subject to data consistency using conjugate-gradient method and use simulation to set the parameters of the proposed method (e.g., iteration number). We apply our method to reconstruct undersampled Cardiac Cine MRI data with and without sparsifying transform, successfully. The use of fuzzy clustering as an intermediate tool to study complicated phenomena by HMM, applicability to non-dynamic MRI data and simplicity can be accounted as the specifications of the proposed method.

*Greedy Deconvolution of Point-like Objects by Dirk A. Lorenz, Dennis Trede. The abstract reads:

The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. In [1] a sufficient condition for exact recovery is derived, in [2] the authors transfer it to noisy signals. We will use OMP for reconstruction of an inverse problem, namely the deconvolution problem. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by incoherence. This idea cannot be transfered to ill-posed inverse problems since here the atoms are typically far from orthogonal: The illposedness of the (typically compact) operator causes that the correlation of two distinct atoms probably gets huge, i.e. that two atoms can look much alike. Therefore in [3], [4] the authors derive a recovery condition which uses the kind of structure one assumes on the signal and works without the concept of coherence. In this paper we will transfer these results to noisy signals. For our source we assume that it consists of a superposition of point-like objects with an a-priori known distance. We will apply it exemplarily to Dirac peaks convolved with Gaussian kernel as used in mass spectrometry.

Circulant and Toeplitz Matrices in Compressed Sensing by Holger Rauhut. The abstract reads:

Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant and Toeplitz matrices in connection with recovery by ℓ1-minization. In contrast to recent work in this direction we allow the use of an arbitrary subset of rows of a circulant and Toeplitz matrix. Our recovery result predicts that the necessary number of measurements to ensure sparse reconstruction by ℓ1-minimization with random partial circulant or Toeplitz matrices scales linearly in the sparsity up to a log-factor in the ambient dimension. This represents a significant improvement over previous recovery results for such matrices. As a main tool for the proofs we use a new version of the non-commutative Khintchine inequality.

Structured Sparsity: from Mixed Norms to Structured Shrinkage by Matthieu Kowalski, Bruno Torrésani. The abstract reads:

Sparse and structured signal expansions on dictionaries can be obtained through explicit modeling in the coefficient domain. The originality of the present contribution lies in the construction and the study of generalized shrinkage operators, whose goal is to identify structured significance maps. These generalize Group LASSO and the previously introduced Elitist LASSO by introducing more flexibility in the coefficient domain modeling. We study experimentally the performances of corresponding shrinkage operators in terms of significance map estimation in the orthogonal basis case. We also study their performance in the overcomplete situation, using iterative thresholding.

*Sparse filter models for solving permutation indeterminacy in convolutive blind source separation by Prasad Sudhakar, Rémi Gribonval. The abstract reads:

Frequency-domain methods for estimating mixing filters in convolutive blind source separation (BSS) suffer from permutation and scaling indeterminacies in sub-bands. Solving these indeterminacies are critical to such BSS systems. In this paper, we propose to use sparse filter models to tackle the permutation problem. It will be shown that the ℓ1-norm of the filter matrix increases with permutations and with this motivation, an algorithm is then presented which aims to solve the permutations in the absence of any scaling. Experimental evidence to show the behaviour of ℓ1-norm of the filter matrix to sub-band permutations is presented. Then, the performance of our proposed algorithm is presented, both in noiseless and noisy cases.

*Minimization of a sparsity promoting criterion for the recovery of complex-valued signalsby Lotfi Chaâri, Jean-Christophe Pesquet, Amel Benazza-Benyahia, Philippe Ciuciu. The abstract reads:

Ill-conditioned inverse problems are often encountered in signal/image processing. In this respect, convex objective functions including a sparsity promoting penalty term can be used. However, most of the existing optimization algorithms were developed for real-valued signals. In this paper, we are interested in complex-valued data. More precisely, we consider a class of penalty functions for which the associated regularized minimization problem can be solved numerically by a forward-backward algorithm. Functions within this class can be used to promote the sparsity of the solution. An application to parallel Magnetic Resonance Imaging (pMRI) reconstruction where complex-valued images are reconstructed is considered.

What I am interesting in is "are there other applications whose outputs are also complex-valued".

*A Compressed Sensing Approach for Biological Microscopy Image Denoisingby Marcio M. Marim, Elsa D. Angelini , Jean-Christophe Olivo-Marin. The abstract reads:

Compressed Sensing (CS) provides a new framework for signal sampling, exploiting redundancy and sparsity in incoherent bases. For images with homogeneous objects and background, CS provides an optimal reconstruction framework from a set of random projections in the Fourier domain, while constraining bounded variations in the spatial domain. In this paper, we propose a CS-based method to simultaneously acquire and denoise data based on statistical properties of the CS optimality, signal modeling and characteristics of noise reconstruction. Our approach has several advantages over traditional denoising methods, since it can under-sample, recover and denoise images simultaneously. We demonstrate with simulated and practical experiments on fluorescence images that we obtain images with similar or increased SNR even with reduced exposure times. Such results open the gate to new mathematical imaging protocols, offering the opportunity to reduce exposure time along with photo-toxicity and photo-bleaching and assist biological applications relying on fluorescence microscopy.

Phase Transitions for Restricted Isometry Properties by Jeffrey D. Blanchard , Coralia Cartis , Jared Tanner. The abstract reads:

Currently there is no framework for the transparent comparison of sparse approximation recoverability results derived using different methods of analysis. We cast some of the most recent recoverability results for ℓ1-regularization in terms of the phase transition framework advocated by Donoho. To allow for quantitative comparisons across different methods of analysis a particular random matrix ensemble must be selected; here we focus on Gaussian random matrices. Methods of analysis considered include the Restricted Isometry Property of Candes and Tao, geometric covering arguments of Rudelson and Vershynin, and convex polytopes formulations of Donoho.

Sparsity Measure and the Detection of Significant Data by Abdourrahmane Atto, Dominique Pastor, Grégoire Mercier. The abstract reads:

The paper provides a formal description of the sparsity of a representation via the detection thresholds. The formalism proposed derives from theoretical results about the detection of significant coefficients when data are observed in presence of additive white Gaussian noise. The detection thresholds depend on two parameters describing the sparsity degree for the representation of a signal. The standard universal and minimax thresholds correspond to detection thresholds associated with different sparsity degrees.

Sparsity hypotheses for robust estimation of the noise standard deviation in various signal processing applications by Dominique Pastor, Francois-Xavier Socheleau, Abdeldjalil Aïssa-El-Bey. The abstract reads:

This paper concerns the problem of estimating the noise standard deviation in different signal processing applications. The presented estimator derives from recent results in robust statistics based on sparsity hypotheses. More specifically, these theoretical results make the link between a standard problem in robust statistics (the estimation of the noise standard deviation in presence of outliers) and sparsity hypotheses. The estimator derived from these theoretical results can be applied to different signal processing applications where estimation of the noise standard deviation is crucial. In the present paper, we address speech denoising and Orthogonal Frequency Division Multiple Access (OFDMA). A relevant application should also be Communication Electronic Support (CES). For such applications, the algorithm proposed is a relevant alternative to the median absolute deviation (MAD) estimator.

Sparse Super-Resolution with Space Matching Pursuits by Guoshen Yu, Stéphane Mallat. The abstract reads:

Super-resolution image zooming is possible when the image has some geometric regularity. Directional interpolation algorithms are used in industry, with ad-hoc regularity measurements. Sparse signal decompositions in dictionaries of curvelets or bandlets find indirectly the directions of regularity by optimizing the sparsity. However, super-resolution interpolations in such dictionaries do not outperform cubic spline interpolations. It is necessary to further constraint the sparse representation, which is done through projections over structured vector spaces. A space matching pursuit algorithm is introduced to compute image decompositions over spaces of bandlets, from which a super-resolution image zooming is derived. Numerical experiments illustrate the efficiency of this super-resolution procedure compared to cubic spline interpolations.

How to use the iterative hard thresholding algorithm by Thomas Blumensath, Michael E Davies. The abstract reads:

Several computationally efficient algorithms have been shown to offer near optimal recovery of sparse signals from a small number of linear measurements. However, whilst many of the methods have similar guarantees whenever the measurements satisfy the so called restricted isometry property, empirical performance of the methods can vary significantly in a regime in which this condition is not satisfied. We here modify the Iterative Hard Thresholding algorithm by including an automatic step-size calculation. This makes the method independent from an arbitrary scaling of the measurement system and leads to a method that shows state of the art empirical performance. What is more, theoretical guarantees derived for the unmodified algorithm carry over to the new method with only minor changes.

Freely Available, Optimally Tuned Iterative Thresholding Algorithms for Compressed Sensing by Arian Maleki , David L. Donoho. The abstract reads:

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the optimally tuned implementations freely available at sparselab.stanford.edu; they can be used 'out of the box' with no user input: it is not necessary to select thresholds or know the likely degree of sparsity. Our class of algorithms includes iterative hard and soft thresholding with or without relaxation, as well as CoSaMP, Subspace Pursuit and some natural extensions. As a result, our optimally tuned algorithms dominate such proposals. Our notion of optimality is defined in terms of phase transitions, i.e. we maximize the number of nonzeros at which the algorithm can successfully operate. We show that the phase transition is a well-defined quantity with our suite of random underdetermined linear systems. Our tuning gives the highest transition possible within each given class of algorithms. We verify by extensive computation the robustness of our recommendations to the amplitude distribution of the nonzero coefficients as well as the matrix ensemble defining the underdetermined system. Several specific findings are established. (a) For all algorithms the worst amplitude
distribution for nonzeros is generally the constantamplitude random-sign distribution; where all nonzeros are the same size. (b) Various random matrix ensembles give the same phase transitions; random partial isometries give different transitions and require different tuning; (c) Optimally tuned Subspace Pursuit dominates optimally tuned CoSaMP, particularly so when the system is almost square. (d) For randomly decimated partial Fourier transform sampling, our recommended Iterative Soft Thresholding gives extremely good performance, making more complex algorithms like CoSaMP and Subspace Pursuit relatively pointless.

*Sparse representations versus the matched filter by F. Martinelli, J.L. Sanz. The abstract reads:

We have considered the problem of detection and estimation of compact sources immersed in a background plus instrumental noise. Sparse approximation to signals deals with the problem of finding a representation of a signal as a linear combination of a small number of elements from a set of signals called dictionary. The estimation of the signal leads to a minimization problem for the amplitude associated to the sources. We have developed a methodology that minimizes the lp-norm with a constraint on the goodness-of-fit and we have compared different norms against the matched filter.

*Image Restoration with Compound Regularization Using a Bregman Iterative Algorithm by Manya V. Afonso, José M. Bioucas-Dias, Mario A. T. Figueiredo. The abstract reads:

Some imaging inverse problems may require the solution to simultaneously exhibit properties that are not enforceable by a single regularizer. One way to attain this goal is to use a linear combinations of regularizers, thus encouraging the solution to simultaneously exhibit the characteristics enforced by each individual regularizer. In this paper, we address the optimization problem resulting from this type of compound regularization using the split Bregman iterative method. The resulting algorithm only requires the ability to efficiently compute the denoising operator associated to each involved regularizer. Convergence is guaranteed by the theory behind the Bregman iterative approach to solving constrained optimization problems. In experiments with images that are simultaneously sparse and piece-wise smooth, the proposed algorithm successfully solves the deconvolution problem with a compound regularizer that is the linear combination of the ℓ1 and total variation (TV) regularizers. The lowest MSE obtained with the (ℓ1+TV) regularizer is lower than that obtained with TV or ℓ1 alone, for any value of the corresponding regularization parameters.

Notes:
1. Bregman iteration / split Bregman iterative method which can be found in "The Split Bregman Method for L1 Regularized Problems" by Tom Goldstein, Stanley Osher;
2. linear combinations of "simple" regularizers ("An iterative algorithm for linear inverse problems with compound regularizers" by J. Bioucas-Dias and M. Figueiredo)
3. The optimal values of the regularization parameters which led to the lowest mean square error are decided by hand tuning. Can they be decided adaptively or by the local info of the image?
4. This paper is very similar to A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data by Junfeng Yang, Yin Zhang and Wotao Yin.

Some SPARS'09 papers about CS (1)

Several papers appeared on my radar screen most of them will be featured in the upcoming SPARS'09 conference:

Distributed algorithms for basis pursuit (also here) by João F. C. Mota, João M. F. Xavier, Pedro M. Q. Aguiar, Markus Püscheldd. The abstract reads:

The Basis Pursuit (BP) problem consists in finding a least l1 norm solution of the underdetermined linear system Ax = b. It arises in many areas of electrical engineering and applied mathematics. Applications include signal compression and modeling, estimation, fitting, and compressed sensing. In this paper, we explore methods for solving the BP in a distributed environment, i.e., when the computational resources and the matrix A are distributed over several interconnected nodes. Special instances of this distributed framework include sensor networks and distributed memory and/or processor platforms. We consider two distribution paradigms: either the columns or the rows of A are distributed across the nodes. The several algorithms that we present impose distinct requirements on the degree of connectivity of the network and the per-node computational complexity.

Compressed sensing for radio interferometry : prior-enhanced Basis Pursuit imaging techniques by Yves Wiaux, Laurent Jacques, Gilles Puy, Anna Scaife, Pierre Vandergheynst. The abstract reads:

We propose and assess the performance of new imaging techniques for radio interferometry that rely on the versatility of the compressed sensing framework to account for prior information on the signals. The present manuscript represents a summary of recent work.

Solving Sparse Linear Inverse Problems: Analysis of Reweighted l1 and l2 Methods by David Wipf , Srikantan Nagarajan. The abstract reads:

A variety of practical methods have recently been introduced for finding maximally sparse representations from overcomplete dictionaries, a central computational task in compressed sensing and source localization applications as well as numerous others. Many of the underlying algorithms rely on iterative reweighting schemes that produce more focal estimates as optimization progresses. Two such variants are iterative reweighted l1 and l2 minimization; however, some properties related to convergence and sparse estimation, as well as possible generalizations, are still not clearly understood or fully exploited. In this paper, we make the distinction between separable and nonseparable iterative reweighting algorithms. The vast majority of existing methods are separable, meaning the weighting of a given coefficient at each iteration is only a function of that individual coefficient from the previous iteration (as opposed to dependency on all coefficients). We examine two such separable reweighting schemes: an l2 method from Chartand and Yin (2008) and an l1 approach from Cand`es et al. (2008), elaborating on convergence results and explicit connections between them. We then explore an interesting non-separable variant that can be implemented via either l2 or l1 reweighting and show several desirable properties relevant to sparse recovery. For the former, we show a direct connection with Chartrand and Yin's approach. For the latter, we demonstrate two desirable properties: (i) each iteration can only improve the sparsity and (ii), for any dictionary and sparsity profile, there will always exist cases where non-separable l1 reweighting improves over standard l1 minimization.

Stability of l1 minimisation in compressed sensing by Przemyslaw Wojtaszczyk. The abstract reads:

We discuss known results (c.f. [16, 6]) about stability of l1 minimisation (denoted \Delta_1) with respect to the measurement error and how those results depend on the measurement matrix \Phi. Then we produce a large class of measurement matrices \Phi for which we can apply results from [16] so we have estimate
\Delta_1(\Phi(x) + r) − x_2 \le C(r_2 + k^(−1/2) \sigma^1_k(x)). (1)
We conclude with a modification of l1 minimisation which gives (1) for most random measurement matrices considered in compressed sensing literature. We also discuss stability of instance optimality in probability.

Recovery of Non-Negative Signals from Compressively Sampled Observations Via Non-Negative Quadratic Programming by Paul O’Grady and Scott Rickard . The abstract reads:

The new emerging theory of Compressive Sampling has demonstrated that by exploiting the structure of a signal, it is possible to sample a signal below the Nyquist rate and achieve perfect reconstruction. In this paper, we consider a special case of Compressive Sampling where the uncompressed signal is non-negative, and propose an extension of Non-negative Quadratic Programming - which utilises Iteratively Reweighted Least Squares - for the recovery of non-negative minimum lp-norm solutions, 0 \le p \le 1. Furthermore, we investigate signal recovery performance where the sampling matrix has entries drawn from a Gaussian distribution with decreasing number of negative values, and demonstrate that - unlike standard Compressive Sampling - the standard Gaussian distribution is unsuitable for this special case.

Compressible image reconstruction via a TVL1-L2 model

In A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data by Junfeng Yang*, Yin Zhang and Wotao Yin, one reconstruction model is mentioned:

Happy Birthday to Myself

Another birthday, and happy birthday to myself.

Thanks very much to my parents, espcially my mother. Thanks for your self-giving love.
Thanks all my friends for your support and help.

祝我:

身体健康! 万事如意! 笑口常开! ^_^

Stephen Boyd's courses videos, Wavelet Tour site,

Stephen Boyd's excellent class about "Convex Optimization" can be found here. Some other amazing course videos are also available there.

One classic wavelet book written by Stéphane Mallat has published its third edition. The site supporting this book is at:

http://www.wavelet-tour.com/

It has all the matlab code associated with the figures in the book. (I think I should read this book sometime.)

Compressive-Sensing Workshop (2009)

The schedule and list of presentation of the Compressive Sensing Workshop is available here. Lots of goodies.