Three problems in compressive sensing, namely, recovery of sparse signals from noise-free measurements, recovery of sparse signals from noisy measurements, and recovery of so called block-sparse signals from noisy measurements, are investigated. In Chapter 2, the reconstruction of sparse signals from noise-free measurements is investigated and three algorithms are developed. The first and second algorithms minimize the approximate L0 and Lp pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasi-Newton algorithm. An efficient line search based on Banach's fixed-point theorem is developed and applied in the second algorithm. The third algorithm minimizes the approximate Lp pseudonorm in the null space by using a sequential conjugate-gradient (CG) algorithm. Simulation results are presented which demonstrate that the proposed algorithms yield improved signal reconstruction performance relative to that of the iterative reweighted (IR), smoothed L0 (SL0), and L1-minimization based algorithms. They also require a reduced amount of computations relative to the IR and L1-minimization based algorithms. The Lp-minimization based algorithms require less computation than the SL0 algorithm. In Chapter 3, the reconstruction of sparse signals and images from noisy measurements is investigated. First, two algorithms for the reconstruction of signals are developed by minimizing an Lp-pseudonorm regularized squared error as the objective function using the sequential optimization procedure developed in Chapter 2. The first algorithm minimizes the objective function by taking steps along descent directions that are computed in the null space of the measurement matrix and its complement space. The second algorithm minimizes the objective function in the time domain by using a CG algorithm. Second, the well known total variation (TV) norm has been extended to a nonconvex version called the TVp pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVp-pseudonorm regularized squared error using a sequential Fletcher-Reeves' CG algorithm. Simulation results are presented which demonstrate that the first two algorithms yield improved signal reconstruction performance relative to the IR, SL0, and L1-minimization based algorithms and require a reduced amount of computation relative to the IR and L1-minimization based algorithms. The TVp-minimization based algorithm yields improved image reconstruction performance and a reduced amount of computation relative to Romberg's algorithm. In Chapter 4, the reconstruction of so-called block-sparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p pseudonorm, and an algorithm based on the minimization of an L2/p-pseudonorm regularized squared error is developed. The minimization is carried out using a sequential Fletcher-Reeves' CG algorithm and the line search described in Chapter 2. A reweighting technique for the reduction of amount of computation and a method to use prior information about the locations of nonzero blocks for the improvement in signal reconstruction performance are also proposed. Simulation results are presented which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to the L2/1-minimization based, block orthogonal matching pursuit, IR, and L1-minimization based algorithms. / Graduate

To address the scale mountain pine beetle (MPB) outbreak in British Columbia, salvage has become fully integrated with timber supply strategies. The objective of this thesis is to assess the economic impact of different salvage strategies depending on different attack levels, decay rates, and stakeholder discount rates. The study area is located in N.E. British Columbia where the MPB has not yet reached its peak and where susceptible to attack stands account for 40% of the area. Salvage strategies were modelled with a timber supply model (Woodstock) which uses a linear programming type II optimization approach. Performance of the model was assessed over a range of indicators such as NPV, profit, salvage proportion, species composition, inventory levels, and non-recoverable volume. Sensitivity analyses were conducted on harvest flow, discount rate, and ending inventory. The model was very sensitive to the intensity of attack and less sensitive to the decay level. The high level of attack resulted in large volume losses, mostly as un-salvaged inventory. Although allowable annual cut (AAC) uplifts have an economic benefit, they do not necessarily maximize the salvage of pine. Non-pine species are an important component of the salvage and these species are also essential for the future timber supply. If the objective is to ensure quality and quantity of the future forest, policies have to complement AAC uplifts by strongly encouraging the salvage of mainly pine-leading stands and management options that minimize the “by-catch” of non-pine species and minimize destruction of advanced regeneration during salvage. However, this has an opportunity cost for the private industry where the objective is to maximize profit. If the salvage strategy focuses on decreasing the impact on cash flows, achieving desirable ending inventory levels, avoiding salvage of stands after shelf-life, and reducing impact on non-attack species, then the current harvest level will likely lead to a mid-term timber supply fall-down. Using the fibre for bioenergy production is an alternative if managing for bioenergy can be integrated into harvest operations. However, unlike mill residues, the bioenergy supply has to fully account for harvest and transportation costs of dead wood to the mill.

To address the scale mountain pine beetle (MPB) outbreak in British Columbia, salvage has become fully integrated with timber supply strategies. The objective of this thesis is to assess the economic impact of different salvage strategies depending on different attack levels, decay rates, and stakeholder discount rates. The study area is located in N.E. British Columbia where the MPB has not yet reached its peak and where susceptible to attack stands account for 40% of the area. Salvage strategies were modelled with a timber supply model (Woodstock) which uses a linear programming type II optimization approach. Performance of the model was assessed over a range of indicators such as NPV, profit, salvage proportion, species composition, inventory levels, and non-recoverable volume. Sensitivity analyses were conducted on harvest flow, discount rate, and ending inventory. The model was very sensitive to the intensity of attack and less sensitive to the decay level. The high level of attack resulted in large volume losses, mostly as un-salvaged inventory. Although allowable annual cut (AAC) uplifts have an economic benefit, they do not necessarily maximize the salvage of pine. Non-pine species are an important component of the salvage and these species are also essential for the future timber supply. If the objective is to ensure quality and quantity of the future forest, policies have to complement AAC uplifts by strongly encouraging the salvage of mainly pine-leading stands and management options that minimize the “by-catch” of non-pine species and minimize destruction of advanced regeneration during salvage. However, this has an opportunity cost for the private industry where the objective is to maximize profit. If the salvage strategy focuses on decreasing the impact on cash flows, achieving desirable ending inventory levels, avoiding salvage of stands after shelf-life, and reducing impact on non-attack species, then the current harvest level will likely lead to a mid-term timber supply fall-down. Using the fibre for bioenergy production is an alternative if managing for bioenergy can be integrated into harvest operations. However, unlike mill residues, the bioenergy supply has to fully account for harvest and transportation costs of dead wood to the mill.

To address the scale mountain pine beetle (MPB) outbreak in British Columbia, salvage has become fully integrated with timber supply strategies. The objective of this thesis is to assess the economic impact of different salvage strategies depending on different attack levels, decay rates, and stakeholder discount rates. The study area is located in N.E. British Columbia where the MPB has not yet reached its peak and where susceptible to attack stands account for 40% of the area. Salvage strategies were modelled with a timber supply model (Woodstock) which uses a linear programming type II optimization approach. Performance of the model was assessed over a range of indicators such as NPV, profit, salvage proportion, species composition, inventory levels, and non-recoverable volume. Sensitivity analyses were conducted on harvest flow, discount rate, and ending inventory. The model was very sensitive to the intensity of attack and less sensitive to the decay level. The high level of attack resulted in large volume losses, mostly as un-salvaged inventory. Although allowable annual cut (AAC) uplifts have an economic benefit, they do not necessarily maximize the salvage of pine. Non-pine species are an important component of the salvage and these species are also essential for the future timber supply. If the objective is to ensure quality and quantity of the future forest, policies have to complement AAC uplifts by strongly encouraging the salvage of mainly pine-leading stands and management options that minimize the “by-catch” of non-pine species and minimize destruction of advanced regeneration during salvage. However, this has an opportunity cost for the private industry where the objective is to maximize profit. If the salvage strategy focuses on decreasing the impact on cash flows, achieving desirable ending inventory levels, avoiding salvage of stands after shelf-life, and reducing impact on non-attack species, then the current harvest level will likely lead to a mid-term timber supply fall-down. Using the fibre for bioenergy production is an alternative if managing for bioenergy can be integrated into harvest operations. However, unlike mill residues, the bioenergy supply has to fully account for harvest and transportation costs of dead wood to the mill. / Forestry, Faculty of / Graduate