Mohammad Tofighi

Evaluation of Dike-Type Causeway Impacts on the Flow and Salinity Regimes in Urmia Lake, Iran

ABSTRACT Urmia Lake, located in a closed basin in north-west Iran, is the largest lake (5000–6000 km2) in the Middle East. It is very saline with total dissolved salts reaching 200 g/l compared with a normal seawater salinity of about 35 g/l. The construction of a causeway, which was initiated in 1979 but then abandoned until the early 2000s, is near completion and will provide road access between the western and eastern provinces. The causeway has an opening 1.25 km long and divides Urmia Lake into a northern and southern basin and restricts water exchange. The flow and salinity regimes are affected by the presence of this new causeway, and there are concerns over the well being of the Artemia population. This study investigates the effects of the construction of the causeway on flow and salinity regimes, considers remedial actions, and examines the effects of climatic variability on salinity and flow. Flow and salinity regimes were numerically simulated by using a commercially available two and three-dimensional (2D and 3D) MIKE model. The validity of the numerical model was assessed through sensitivity analysis of the model and comparing the simulated results against field measurements; the 3D model provided the higher correlation between simulated and actual data. Wind input was the main climatic and hydrologic factor influencing flow regime while river discharge, evaporation and rainfall were the key parameters affecting salinity distribution in the lake models. The 3D model was subsequently used to predict lake conditions in typical dry, wet and normal climates, to examine the environmental impacts from the new causeway, and to evaluate possible improvements that some remedial measures may provide.

Projections onto convex sets (POCS) based optimization by lifting

Summary form only given. A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in RN+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p <; 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems.

Projection-Based Wavelet Denoising [Lecture Notes]

In this lecture note, we describe a wavelet domain denoising method consisting of making orthogonal projections of wavelet (subbands) signals of the noisy signal onto an upside down pyramid-shaped region in a multidimensional space. Each horizontal slice of the upside down pyramid is a diamond shaped region and it is called an -ball. The upside down pyramid is called the epigraph set of the -norm cost function. We show that the method leads to soft-thresholding as in standard wavelet denoising methods. Orthogonal projection operations automatically determine the soft-threshold values of the wavelet signals.

Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

In this paper, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the Epigraph Set of Total Variation (ESTV) function. This set does not need a prescribed upper bound on the Total Variation (TV) of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both the TV of the image and the blurring filter are regularized using the ESTV set. Both the phase information set and the ESTV are closed and convex sets. Therefore they can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.

Denoising using projections onto the epigraph set of convex cost functions

A new denoising algorithm based on orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and feasibility sets corresponding to the cost function using the epigraph concept are defined. As the utilized cost function is a convex function in RN, the corresponding epigraph set is also a convex set in RN+1. The denoising algorithm starts with an arbitrary initial estimate in RN+1. At each step of the iterative denoising, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The method provides globally optimal solutions for total-variation, ℓ1, ℓ2, and entropic cost functions.

Range resolution improvement in FM-based passive radars using deconvolution

FM-based passive bistatic radar (PBR) systems suffer from low range resolution because of the low baseband bandwidth of commercial FM broadcasts. In this paper, we propose a range resolution improvement method using deconvolution. The output of the PBR matched filter is processed using a deconvolution algorithm which assumes that targets are isolated, i.e., sparse in the range domain. The deconvolution algorithm is iterative and was implemented by performing successive orthogonal projections onto supporting hyperplanes of the epigraph set of a convex cost function. Simulation examples are presented.

Range-Doppler radar target detection using compressive sensing

Compressive sensing (CS) idea enables the reconstruction of a sparse signal from small number of measurements. CS approach has many applications in many areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented.

Deconvolution using projections onto the epigraph set of a convex cost function

A new deconvolution algorithm based on making orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost function and observations are defined. If the utilized cost function is convex in RN, the corresponding epigraph set is also convex in RN+1. The deconvolution algorithm starts with an arbitrary initial estimate in RN+1. At each iteration cycle of the algorithm, first deconvolution projections are performed onto the hyperplanes representing observations, then an orthogonal projection is performed onto epigraph of the cost function. The method provides globally optimal solutions for total variation, l1, l2, and entropic cost functions.

Projections onto the epigraph set of the filtered variation function based deconvolution algorithm

A new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in RN, then the corresponding epigraph set is also a convex set in the lifted set in RN+1. At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in RN+1, first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image.

Target detection using sparsity based deconvolution in passive bistatic radars

We introduce a sparsity based deconvolution scheme to improve the range resolution of passive bistatic radar (PBR) systems. The two-dimensional matched filter output of a PBR system is further analyzed as a deconvolution problem. The deconvolution algorithm is based on making projections onto hyperplanes representing the time delay of a target and the epigraph set of a convex cost function such as the l1 norm. The iterative algorithm is globally convergent because all constraint sets are closed and convex. Simulation results in a FM based PBR system are presented. The proposed method performs better than frequency domain deconvolution methods.