diff --git a/ext/RegularizedLeastSquaresGPUArraysExt/ProxL21.jl b/ext/RegularizedLeastSquaresGPUArraysExt/ProxL21.jl
new file mode 100644
index 00000000..15759ced
--- /dev/null
+++ b/ext/RegularizedLeastSquaresGPUArraysExt/ProxL21.jl
@@ -0,0 +1,11 @@
+function RegularizedLeastSquares.proxL21!(x::vecT, λ::T, slices::Int64) where {T, vecT <: Union{AbstractGPUVector{T}, AbstractGPUVector{Complex{T}}}}
+  sliceLength = div(length(x),slices)
+  groupNorm = [norm(x[i:sliceLength:end]) for i=1:sliceLength]
+
+  gpu_call(x, λ, groupNorm, sliceLength) do ctx, x_, λ_, groupNorm_, sliceLength_
+    i = @linearidx(x_)
+    @inbounds x_[i] = x_[i]*max( (groupNorm_[mod1(i,sliceLength_)]-λ_)/groupNorm_[mod1(i,sliceLength_)],0)
+    return nothing
+  end
+  return x
+end
\ No newline at end of file
diff --git a/ext/RegularizedLeastSquaresGPUArraysExt/RegularizedLeastSquaresGPUArraysExt.jl b/ext/RegularizedLeastSquaresGPUArraysExt/RegularizedLeastSquaresGPUArraysExt.jl
index 9cffd2ad..83581153 100644
--- a/ext/RegularizedLeastSquaresGPUArraysExt/RegularizedLeastSquaresGPUArraysExt.jl
+++ b/ext/RegularizedLeastSquaresGPUArraysExt/RegularizedLeastSquaresGPUArraysExt.jl
@@ -1,8 +1,9 @@
 module RegularizedLeastSquaresGPUArraysExt
 
-using RegularizedLeastSquares, GPUArrays
+using RegularizedLeastSquares, RegularizedLeastSquares.LinearAlgebra, GPUArrays
 
 include("Utils.jl")
 include("ProxTV.jl")
+include("ProxL21.jl")
 
 end
\ No newline at end of file
diff --git a/src/proximalMaps/ProxNuclear.jl b/src/proximalMaps/ProxNuclear.jl
index 46ac0e6d..f8e7c14d 100644
--- a/src/proximalMaps/ProxNuclear.jl
+++ b/src/proximalMaps/ProxNuclear.jl
@@ -26,7 +26,7 @@ performs singular value soft-thresholding - i.e. the proximal map for the nuclea
 function prox!(reg::NuclearRegularization, x::Union{AbstractArray{T}, AbstractArray{Complex{T}}}, λ::T) where {T <: Real}
   U,S,V = svd(reshape(x, reg.svtShape))
   prox!(L1Regularization, S, λ)
-  copyto!(x, vec(U*Matrix(Diagonal(S))*V'))
+  copyto!(x, vec(U*Diagonal(S)*V'))
   return x
 end
 
diff --git a/src/proximalMaps/ProxProj.jl b/src/proximalMaps/ProxProj.jl
index df974382..6a6bc99b 100644
--- a/src/proximalMaps/ProxProj.jl
+++ b/src/proximalMaps/ProxProj.jl
@@ -5,12 +5,12 @@ struct ProjectionRegularization <: AbstractProjectionRegularization
 end
 ProjectionRegularization(; projFunc::Function=x->x, kargs...) = ProjectionRegularization(projFunc)
 
-function prox!(reg::ProjectionRegularization, x::Vector{Tc}) where {T, Tc <: Union{T, Complex{T}}}
+function prox!(reg::ProjectionRegularization, x::AbstractArray{Tc}) where {T, Tc <: Union{T, Complex{T}}}
   copyto!(x, reg.projFunc(x))
   return x
 end
 
-function norm(reg::ProjectionRegularization, x::Vector{Tc}) where {T, Tc <: Union{T, Complex{T}}}
+function norm(reg::ProjectionRegularization, x::AbstractArray{Tc}) where {T, Tc <: Union{T, Complex{T}}}
   y = copy(x)
   copyto!(y, prox!(reg, y))
   if y != x
diff --git a/test/testProxMaps.jl b/test/testProxMaps.jl
index eaf1522b..ced2f06d 100644
--- a/test/testProxMaps.jl
+++ b/test/testProxMaps.jl
@@ -285,12 +285,12 @@ function testConversion()
         true
       catch e
         false
-      end skip = in(prox, [LLRRegularization, NuclearRegularization])
+      end skip = in(prox, [LLRRegularization])
       @test try norm(prox, zeros(xType, 10), lambdaType(0.0); shape=(2, 5), svtShape=(2, 5))
         true
       catch e
         false
-      end skip = in(prox, [LLRRegularization, NuclearRegularization])
+      end skip = in(prox, [LLRRegularization])
     end
   end
 end