
Submitted by
Assigned_Reviewer_2
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
The authors present an unnamed algorithm for
recovering a degree three tensor from a noisy version, where the noise is
due to (a) slice misalignment and (b) sparse noise. The authors present a
loss function for the model which they optimize by an ADMMinspired
gradient descent heuristic. The authors compare their method on real and
synthetic image data to different implementations of RASL and and an
algorithm from [14] which they call "Li's work" and show that their
algorithm has lower recovery error.
The paper is clearly written
and the idea of performing alignment and denoising on multiple images at
once seems to be novel, while the reviewer is not a full expert on tensor
methods in image processing and cannot finally settle the question of
originality of the application. The heuristic used in the optimization
method is somewhat original but can be obtained by putting known methods
together.
It surprises the reviewer that theorem 1 on global
convergence claims to be true without further assumptions on the noise
model or the underlying tensor. Reading through the appendix reveals that
there are indeed conditions depending on those. Maybe the authors can
clarify this.
Also, the authors mention TILT which could be used
slicewise. Maybe as a sanity check, a comparison to slicewise TILT could
be added to the experiments.
The significance of the algorithm
relies in my opinion not on the theoretical groundwork which is only
partly new, but mainly on the practical applications, in which it seems to
perform significantly better than standard
methods. Q2: Please summarize your review in 12
sentences
A novel optimization algorithm for simultaneously
rectifying and denoising of degree three tensors which seems to outperform
stateoftheart methods. In this combination, it seems to be novel and
relevant to the NIPS community. Submitted by
Assigned_Reviewer_4
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper proposes a model to simultaneously rectify
and align images via robust lowrank tensor recovery. This model is a
generalization of the corresponding matrix problem studied in TILT [1] and
RASL [6], to the tensor correspondence. This work is actually a
combination of a number of ideas in the existing literature. First, the
model (6) is a generalization of the matrix problem in RASL. Second,
relaxing the tensor rank to the sum of ranks of its unfoldings has been
studied in [10]. Note that in Eq. (7), the L_{(i)} are unfoldings, thus
this is not based on Tucker decomposition. The statement that is 5 lines
before Eq. (7) is not appropriate. Thrid, using ADMM to solve the
resulted convex problem is not new. Similar idea has been studied in [6]
and [11]. Thus, this paper is not of enough contribution in terms of
novelty. The numerical results seem to be interesting though.
Q2: Please summarize your review in 12 sentences
This paper is not of enough contribution in terms of
novelty. The numerical results seem to be interesting
though. Submitted by
Assigned_Reviewer_5
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper is an extension of TILT [1] and RASL [6]
that estimate alignments of images based on a tensor model for a
collection of images.
Given a collection of images, the authors
propose a method for finding a linear transformation that aligns each
image simultaneously taking into account the lowrankness of the true
image as a matrix and the correlation between different images. The
authors formulate this problem as a lowrank tensor recovery problem with
sparse corruption (similar to robust PCA).
An extension of robust
PCA to tensor data was proposed by Li et al. [14] but they did not
optimize the alignments.
Two previous studies that consider the
same alignment model, TILT [1] and RASL [6] consider either the
lowrankness of each image separately or the lowrankness of the
collection of vectorized images, but do not consider the two jointly.
The authors derive a linearized ADM algorithm for the inner
minimization problem and show its convergence. The authors also
empirically demonstrate the advantage of joint lowrank modeling on
several data sets.
The paper is mostly clearly written.
There are some issues I would like the authors to clarify: 1.
If I undderstand correctly, the optimization algorithm discussed in
Section 3.2 is an inner loop that only solves the linearized problem (9).
However the outer loop is not described anyware on this paper. Please
clarify. 2. Please quantitatively evaluate he results of Figures 35.
3. I only see sparse corruptions in Figure 3. How would using a
squared loss as in [1013] change the results of Figures 45?
Q2: Please summarize your review in 12
sentences
This paper is a tensor extension of two previous
studies that simultaneously considers two types of lowrankness in a
collection of images. The paper is mostly clearly written and suitable for
presentation. Submitted by
Assigned_Reviewer_6
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper considers the (unrectified and misaligned)
tensor recovery problem, which is an interesting problem.
Originality: This work extends the matrix case in [1] to the
tensor case. Specifically, it replaces the matrix nuclear norm in Eq. (3)
of [1] by the tensor nuclear norm. I am afraid that this type of extension
may not be treated as a substantial contribution any more since similar
extensions have appeared in many early papers like [1014, etc]. The new
staff beyond this extension seems to consider the misalignment issue in
tensors. The technique used to deal with unrectification and misalignment
actually follows [1] as well. This paper just simply splits the tensor
data into matrices and uses the technique proposed in [1] to deal with
uncertification and misalignment in matrices. Although this paper claims
that the proposed method align across images unlike [1], that is just due
to the tensor nuclear norm rather than any new alignment technique.
A variant of the ADMM method is used to solve a key step of the
proposed formulation. This paper claims ADMM is not efficient to solve
(121)  the first subproblem in (12) because (121) does not give a
closed form. To my experiences, if properly introduce new variables into
(11), it can be formulated into a structure good for ADMM (that is, all
subproblems have closed form solutions): you can try duplicate \L and \E
in (11).
The proof for Theorem 1 seems unnecessary. The
convergence for many variants for ADMM, including using the proximal
gradient descent (used in this paper) to replace the exactly solving, has
been shown in many optimization papers already, for example, [A], [B].
Overall, this paper is not of sufficient contribution in term of
originality. My novelty judgement is only based on the aspects of modeling
and algorithm. Contributions in numerical results may be ignored.
Clarity: Some equations are not clear enough, and some
notations are abused apparently in section 3.1. Readers like me have to
read [1] to understand those undefined and unclear notations and
equations. Authors should seriously treat the following issues.  (5)
reuses "\circ" which has been used in (2). Two ``\circ'' actually mean
totally different things. Readers that unfamiliar with [1] may be misled
in (5). Moreover, the followed explanation for "A\circ \Tau" is also
unclear. ``Applying the transformation \tau_i to each matrix A(:,:,i)''
sounds like the matrix multiplication \tau_i A(:,:,i). It actually means
A(\tau_x, \tau_y, i) from [1].  What is the value of ``p'' in two
lines before (5)?  (8) is suddenly relaxed into (9) by using a
``popular'' way. What is the ``popular'' way? No explanation, no
citations. Readers have to figure out it from other papers like [1]. 
The last line of Section 3.1: what is the value of "n". This notation "n"
appears for multiple times before this line. Apparently, they denote
different things.
[A] On the Linear Convergence of the Alternating
Direction Method of Multipliers, Mingyi Hong, ZhiQuan Luo, 2012. [B]
Linearized Alternating Direction Method of Multipliers for Constrained
Linear LeastSquares Problem, Raymond H. Chan1, Min Tao, Xiaoming Yuan,
2012. Q2: Please summarize your review in 12
sentences
This paper is an incremental work from [1]. It is not
of sufficient contribution in term of originality. My novelty judgement is
only based on the aspects of modeling and algorithm. Contributions in
numerical results may be ignored.
Q1:Author
rebuttal: Please respond to any concerns raised in the reviews. There are
no constraints on how you want to argue your case, except for the fact
that your text should be limited to a maximum of 6000 characters. Note
however that reviewers and area chairs are very busy and may not read long
vague rebuttals. It is in your own interest to be concise and to the
point.
 