Mohammad Aghagolzadeh

Compressive Framework for Demosaicing of Natural Images

Typical consumer digital cameras sense only one out of three color components per image pixel. The problem of demosaicing deals with interpolating those missing color components. In this paper, we present compressive demosaicing (CD), a framework for demosaicing natural images based on the theory of compressed sensing (CS). Given sensed samples of an image, CD employs a CS solver to find the sparse representation of that image under a fixed sparsifying dictionary Ψ. As opposed to state of the art CS-based demosaicing approaches, we consider a clear distinction between the interchannel (color) and interpixel correlations of natural images. Utilizing some well-known facts about the human visual system, those two types of correlations are utilized in a nonseparable format to construct the sparsifying transform Ψ. Our simulation results verify that CD performs better (both visually and in terms of PSNR) than leading demosaicing approaches when applied to the majority of standard test images.

Image Super-Resolution via Local Self-Learning Manifold Approximation

This letter proposes a novel learning-based super-resolution method rooted in low dimensional manifold representations of high-resolution (HR) image-patch spaces. We exploit the input image and its different down-sampled scales to extract a set of training sample points using a min-max algorithm. A set of low dimensional tangent spaces is estimated from these samples using the l1 norm graph-based technique to cluster these samples into a set of manifold neighborhoods. The HR image is then reconstructed from these tangent spaces. Experimental results on standard images validate the effectiveness of the proposed method both quantitatively and perceptually.

Adaptive dictionaries for compressive imaging

Compressive imaging reconstructs the original signal by searching through the feasible space for the solution with maximum compactness under a known frame or dictionary. With the extent of available optimization tools, the recovery performance mainly relies on the power of dictionary to sparsely represent the data. Universal dictionaries can be trained from a corpus of natural images or they can be designed through mathematical modeling. However, a problem with universal dictionaries is that they are suboptimal for individual classes of images. To mitigate this suboptimality, we explore ways of adapting the dictionary after the image is sensed using local and non-overlapping sampling matrices. We demonstrate that to prevent the dictionary from becoming biased under the deterministic sensor structure, sampling matrices should have diversity across different locations of the image. The proposed dictionary adaptation along with varying sampling matrices improves the recovery over state-of-the-art universally learned dictionaries of different sizes.

Transitivity matrix of social network graphs

Transitivity in friendship graphs has been well known as a key property of social networks. In this paper, we extend the graph transitivity index by introducing a new characteristic quantity of graphs, namely the transitivity matrix. The transitivity matrix measures the microscopic impact that each link has on the global transitivity index of the graph. We argue that the new transitivity metric is synergetic with key aspects of the social science literature on social network theory, and we show that it can be used as a tool for locating bridges as well as redundant links. This work represents a major departure from the traditional graph transitivity index, which provides a coarse measure for how transitive the overall network is.

Bayer and panchromatic color filter array demosaicing by sparse recovery

The utility of Compressed Sensing (CS) for demosaicing of digital images have been explored by few recent efforts. Most recently, a Compressive Demosaicing [3] framework, based on employing a random panchromatic Color Filter Array (CFA) at the sensing stage, has provided compelling CS-based demosaicing results by visually outperforming other leading techniques. Meanwhile, it is well known that the Bayer pattern is arguably the most popular CFA used in low-cost consumer digital cameras. In this paper, we explore and compare the Bayer and random panchromatic CFA structures using a generic approach for demosaicing of images based on recent advances in the field of CS. In particular, a key objective of this work is to provide a comparative analysis between these two CFA patterns (Bayer and random panchromatic) under the general umbrella of sparse recovery, which represents the cornerstone of CS-based decoding. We demonstrate the viability of the Bayer pattern under certain CS conditions. Meanwhile, we show that a random panchromatic CFA, which meets certain incoherence constraints, can visually outperform a Bayer based sparse recovery. As illustrated in our simulation results, a panchromatic CFA is more consistent in terms of providing better visual quality when tested on a wide range of color images.

Compressive dictionary learning for image recovery

In this paper, we tackle real-time learning of a dictionary D from compressive measurements Y of an image X. Existing dictionary learning algorithms are inapplicable because compressive samples Y = ΦX are incomplete and can be arbitrary linear combinations of different pixels. Our strategy is to learn a dictionary of the form D = ΨΘ, which represents compressible dictionaries with respect to the base dictionary Ψ. We show that our method for learning dictionaries during compressive image recovery can improve the recovery results by up to 3 dBs for general random sampling matrices.

New guarantees for Blind Compressed Sensing

Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS, dictionary learning, a.k.a. sparse coding, has been studied as a matrix factorization problem where its sample complexity, uniqueness and identifiability have been addressed thoroughly. However, in spite of the strong connections between BCS and sparse coding, recent results from the sparse coding problem area have not been exploited within the context of BCS. In particular, prior BCS efforts have focused on learning constrained and complete dictionaries that limit the scope and utility of these efforts. In this paper, we develop new theoretical bounds for perfect recovery for the general unconstrained BCS problem. These unconstrained BCS bounds cover the case of overcomplete dictionaries, and hence, they go well beyond the existing BCS theory. Our perfect recovery results integrate the combinatorial theories of sparse coding with some of the recent results from low-rank matrix recovery. In particular, we propose an efficient CS measurement scheme that results in practical recovery bounds for BCS. Moreover, we discuss the performance of BCS under polynomial-time sparse coding algorithms.

Compressed video sensing using adaptive sampling rate

Compressive video sampling is an application of compressed sensing (CS) theory which samples a signal below the Shannon-Nyquist rate. In this paper, we present a compressed video sensing method that samples the blocks with adaptive sampling rate. The edge of the image is exploited to define a deficiency factor for blocks. Considering this factor, we determine sampling rates independently for each block. The simulation results show that the proposed method outperforms the conventional CS in image quality for the same compression ratio.

Compressive demosaicing for periodic color filter arrays

The utility of Compressed Sensing (CS) for demosaicing of images captured using random panchromatic color filter arrays (CFA) has been investigated in [1]. Meanwhile, most camera manufacturers employ periodic CFAs such as the popular Bayer CFA. In this paper, we derive a CS-based solution to demosaicing images captured using the general class of periodic CFAs. It is well known that periodic CFAs can be designed to effectively separate luminance and chrominance frequency bands [2, 3]. We employ this ability to reduce artifacts associated with luminance-chrominance overlap at the solver side. We show that the modified compressive demo-saicing method coupled with the additional constraint that chrominance channels have smooth surfaces achieves further improved results for most periodic CFAs.

Incoherent color frames for compressive demosaicing

In this paper, we explore the notion of using frames to project sensed colors within their inherently 3D space onto a larger number of color basis vectors. In particular, we develop a new frame design, Incoherent Color Frames (ICF), which can include an arbitrary number of incoherent color vectors. An ICF frame possesses key desired properties including the ability to sparsify colors in 3D and to decorrelate color channels utilizing a spatial-frequency selective strategy. We present a low complexity algorithm for constructing ICF frames targeted for the problem of image demosaicing. Our simulation results show that when incorporating the proposed ICF within a Compressive Demosaicing (CD) framework [8], significant visual improvements can be achieved when compared with traditional and Compressed Sesnsing-based demosaicing solutions.