0316

first paper "Sparse Representation-based Image Deconvolution by Iterative Thresholding" by
M.J. Fadili
abstract reads,
Image deconvolution algorithms with overcomplete sparse representations and fast iterative
thresholding methods are presented. The image to be recovered is assumed to be sparsely rep-
resented in a redundant dictionary of transforms. These transforms are chosen to offer a wider
range of generating atoms; allowing more flexibility in image representation and adaptativity
to its morphological content. The deconvolution inverse problem is formulated as the minimiza-
tion of an energy functional with a sparsity-promoting regularization (e.g. ℓ1 norm of the image
representation coefficients). As opposed to quadratic programming solvers based on the interior
point method, here, recent advances in fast solution algorithms of such problems, i.e. Stagewise
Iterative Thresholding, are exploited to solve the optimization problem and provide fast and
good image recovery results. Some theoretical aspects as well as computational and practical
issues are investigated. Illustrations are provided for potential applicability of the method to
astronomical data.
这篇文章分析了hard threshold + LARS(least angular regression) 和StOMP方法，基本结论是hard threshold 是个好东西。里面有引用了一些hard threshold 收敛性的结论，回头要再好好看看。

second paper "Comparison of few-view CT image reconstruction algorithms by constrained totalvariation minimization based on different sampling bases"
abstract
Abstract— The aim of this paper is to investigate how the
choice of the sampling basis affects the reconstruction results
of constrained total-variation (TV) minimization algorithms
used for few-view computed tomography (CT). The reconstruction
results between the algorithm based on frequency
samples (AFS) and the algorithm based on projection samples
(APS) are compared using numerical simulated data. Under
same conditions, AFS exhibits better results compared with
APS. These experimental results confirm that provided same
conditions, the more incoherence between the basis for sampling
"phi" and the basis of the sparse signal "alpha", the better reconstruction
results of the constrained TV minimization algorithm
can be achieved and better algorithms can be developed with
the basis pairs (phi, alpha).
这篇文章的工作很有意思，对于ct是否适合使用cs 是个引子。

entry 0315

first paper "A Wide-Angle View at Iterated Shrinkage Algorithms" by M. Elad, B. Matalon, J. Shtok, and M. Zibulevsky
abstract 这里的threshold 都是对每个向量中的entry进行操作，其天threshold取决于entry值本身，属于Daubechies的threshold. 这种方法的收敛性是得到保证的，文中讨论了几种跟iterative threshold结合的优化方法。
1 surrogate functions and Proximal-point method， 用一个比目标函数大的函数来替代优化，目的是为了能够简化优化步骤。
2 em and bound-optimization approaches 跟上面方法类似。这个替代函数需要满足三个条件。
3 Focuss or iterative reweighted least square weight 是个类似 z/(1+Z)的结构，z为每个迭代中的解。fixed-point iteration被用来优化。
4 parallel coordinate descent 一种类似art的方法。
5 StOmp属于truncated l2 norm(truncated newton iteration) 优化方法，只更新大于threshold的entries，对于large scale的问题不太适合，而且收敛性也未能保障

second paper "Image reconstruction from a small number of projections" by G T Herman and R Davidi
abstract


主要探讨了 digital assuption of ct ，没有全部理解。 指出tv mini在某些情况下不能exact reconstruction。tumor structure missing。用了跟sidkey 颠倒的优化策略。

third paper "iterative thresholding for sparse appoximation" by Thomas Blumensath and Mike E.Davies
the abstract

主要提出了两种threshold的策略，第一种为Daubechies的threshold，第二种则是一种全局的策略。对于优化 |y - AX|2 + u * |X|1 的好处在于不需要考虑u的大小。